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UBS Center Working Paper Series
Working Paper No. 1, November 2012
Sharing High Growth Across Generations:
Pensions and Demographic Transition in China
Zheng Song
Kjetil Storesletten
Yikai Wang
Fabrizio Zilibotti
About the UBS International Center of Economics in Society
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Sharing High Growth Across
Generations:
Pensions and Demographic
Transition in China
Zheng Song University of
Chicago Booth
Kjetil Storesletten Federal
Reserve Bank of Minneapolis
and CEPR
Yikai Wang University of Zurich
Fabrizio Zilibotti University of
Zurich and UBS International
Center of Economics in Society
Abstract
Intergenerational inequality and old-age poverty are salient issues in contemporary
China. China’s aging population threatens the fiscal sustainability of its pension
system, a key vehicle for intergenerational redistribution. We analyze the positive
and normative effects of alternative pension reforms, using a dynamic general equilibrium model that incorporates population dynamics and produc­tivity growth.
­Although a reform is necessary, delaying its implementation implies large welfare
gains for the (poorer) current generations, imposing only small costs on (richer)
­future generations. In contrast, a fully funded reform harms current generations,
with small gains to future generations. High wage growth is key for these results.
Keywords: China; Credit market imperfections; Demographic transition; Economic
growth; Fully funded system; Inequality; Intergenerational redistribution; Labor
supply; Migration; Pensions; Poverty; Rural-urban reallocation; Total fertility rate;
Wage growth.
JEL classifcation: E21, E24, G23, H55, J11, J13, O43, R23.
Acknowledgements: We thank Philippe Aghion, Chong-En Bai, Tim Besley,
Jimmy Chan, Martin Eichenbaum, Vincenzo Galasso, Chang-Tai Hsieh, Andreas
Itten, Dirk Krueger, Albert Park, Torsten Persson, Richard Rogerson, and seminar
participants at the conference China and the West 1950-2050: Economic Growth,
Demographic Transition and Pensions (University of Zurich, November 21, 2011),
China Economic Summer Institute 2012, Chinese University of Hong Kong, Shanghai University of Finance and Economics, Goethe University of Frankfurt, Hong
Kong University, London School of Economics, Princeton University, Tsinghua Workshop in Macroeconomics 2011, Università della Svizzera Italiana, University of
Mannheim, University of Pennsylvania, and University of Toulouse. Yikai Wang
acknowledges financial support from the Swiss National Science Foundation (grant
no. 100014-122636). Fabrizio Zilibotti acknowledges financial support from the
ERC Advanced Grant IPCDP-229883. The views expressed herein are those of the
authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the
Federal Reserve System.
I.
Introduction
China has grown at stellar rates over the last 30 years. With a GDP per capita
still below 20% of the US level, it still has ample room for further convergence
in technology and productivity. However, the success is imbalanced. The GDP per
capita in urban areas is more than three times as large as in rural areas. Even within
urban areas, the degree of inequality across citizens of different ages and educational
groups is very high. The labor share of output is low and stagnating, corroborating
the perception that the welfare of the majority of the population is not keeping pace
with the high output growth. These observations motivate a growing debate about
which institutional arrangements can allow more people to share the benefits of high
growth.1
Among the various dimensions of the problem, intergenerational inequality is a
salient one. Due to fast productivity growth, the present value of the income of a
young worker who entered the labor force in 2000 is on average about six times as
large as that of a worker who entered in 1970, when China was one of the poorest
countries in the world. On the lower end of the income distribution, this fact implies
that poverty among the elderly is pervasive, especially in rural areas, but also among
low-income urban households who have no sons (who are traditionally responsible
for the support of the elderly) and/or do not receive sizeable transfers from their
children.2
An important aspect of this debate is China’s demographic transition. The total
dependency ratio has fallen from 75% in 1975 to a mere 37% in 2010. This change
is due to the combination of high fertility in the 1960s and the family planning
policies introduced in the 1970s, culminating with the draconian one-child policy in
1978. The expansion of the labor force implied by this transition has contributed
to economic growth. However, China is now at a turning point: by 2040 the oldage dependency ratio will have increased from the current 12% to 39%. The aging
population threatens, on the one hand, the viability of the traditional system of oldage insurance – the share of elderly without children who can actively support and
care for the parents is growing, due to shrinking average family size. On the other
hand, it undermines the fiscal viability of redistributive policies, especially pensions,
which are arguably the most important institutional vehicle for intergenerational
redistribution. In this paper, we analyze the welfare effects of alternative pension
reforms.
Our analysis is based on a dynamic general equilibrium model incorporating a
public pension system. The standard tool for such analyses is the Auerbach and
Kotlikoffhor (1987) model (henceforth the Au-Ko model ) – a multiperiod overlapping generations (OLG) model with endogenous capital accumulation, wage growth,
and an explicit pension system. Our model departs from the canonical Au-Ko model
by embedding some salient structural features of the Chinese economy: the ruralurban transition and a rapid transformation of the urban sector, where state-owned
1 For instance, Wen Jiabao, premier of the State Council of the People’s Republic of China, declared in a
March 14 2012 press conference, “I know that social inequities...have caused the dissatisfaction of the masses.
We must push forward the work on promoting social equity. ...The first issue is the overall development of
the reform of the income distribution system.”
2 Using data from the 2005 Chinese Longitudinal Healthy Longevity Survey, Yang (2011) reports that
survey measures of poverty such as for instance ”inadequate daily living source” (reported by 37% of the
elderly population) or ”not eating meat in a week” (reported by 38% of the elderly population) among
people over 60 correlate strongly with the access to family transfers. The same survey shows that 42% of
the elderly cannot count on significant family transfers; that is, they receive less than 500 RMB per year.
2
enterprises are declining and private entrepreneurial firms are growing. Such a transition is characterized, following Song, Storesletten and Zilibotti (2011), by important
financial and contractual imperfections.
The model bears two key predictions. First, wage growth is delayed: as long as
the transition within the urban sector persists, wage growth is moderate. Yet, as
the transition comes to an end, the model predicts an acceleration of wage growth.
Second, financial imperfections cause a large gap between the rate of return to
industrial investments and the rate of return to which Chinese households have
access. A calibrated version of the model forecasts that wages will grow at an
average of 6.2% until 2030 and slow down rapidly thereafter. GDP growth will also
slow down but is expected to remain as high as 6% per year over the next two
decades. By 2040, China will have converged to about 70% of the level of GDP per
capita of the US.
We use the model to address two related questions: (i) Is a pension system based on
the current rules sustainable? (ii) What are the welfare effects of alternative reforms?
The answer to the first question is clear-cut: the current system is unbalanced and
requires a significant adjustment in either contributions or benefits. We focus on
the benefit margin and consider a benchmark reform reducing the pension payments
to all workers retiring after 2011. The reform does not renege on the outstanding
obligations to current retirees but only changes the entitlements of workers retiring
as of 2012 – this is the pattern of most reforms in OECD countries. This reform
entails a sharp permanent reduction of the replacement rate, from 60% to 40%,
which would allow the accumulation of a large pension fund until 2050 to pay for
the pensions of future generations retiring in times when the dependency ratio will
be much higher than today.
To address the second question, we consider three alternative scenarios. First, we
study the effect of a delayed reform, by which the current rules remain in place until
a future date T , to be followed by a permanent reduction in benefits, to balance
the pension system in the long run. If the reform is delayed until 2040, our model
predicts large welfare gains for the transition generations relative to the draconian
benchmark reform in 2012. Quantitatively, the gains accruing to the cohorts retiring
before 2040 would be equivalent to a 17% increase in their lifetime consumption. The
generations retiring after 2040 would only suffer small additional losses in the form
of an even lower replacement ratio. Second, we consider the effects of switching to
a pure pay-as-you-go (PAYGO) system where the replacement rate is endogenously
determined by the dependency ratio, subject to a balanced budget condition for the
pension system. A PAYGO reform has similar, if more radical, welfare effects as a
delayed reform. Given the demographic transition of China, the PAYGO yields very
generous pensions to early cohorts and severely punishes the generations retiring
after 2050. Both reforms share a common feature: they allow the poorer current
generations to share the benefits of high wage growth with the richer generations that
will enter the labor market when China is a mature economy. Finally, we consider
switching to a fully funded (FF) individual account system, which we label a fully
funded reform. In our model, this system is equivalent to terminating the public
pension system altogether. To honor existing obligations, the government issues
bonds to compensate current workers and retirees for their past contributions. Since
we assume the economy to be dynamically efficient, a standard trade-off emerges: all
generations retiring after 2062 benefit from the fully funded reform, whereas earlier
generations lose.
3
We aggregate the welfare of different cohorts using a utilitarian social planner who
discounts the welfare of future cohorts at reasonable rates. We show that even a
highly forward-looking planner with an annual discount rate as low as 0.5% would
choose to either switch to a PAYGO or delay the implementation of a sustainable
pension reform. Such alternative reforms are preferred to the immediate implementation of the sustainable reform as well as to the fully funded reform. The motive is
the drive to redistribute income from the rich cohorts retiring in the distant future
to the poor cohorts retiring today or in the near future.
These normative predictions run against the common wisdom that switching to a
pre-funded pension system is the best response to adverse demographic dynamics.
For instance, Feldstein (1999), Feldstein and Liebman (2006) and Dunaway and
Arora (2007) argue that a fully funded reform is the best viable option for China.
On the contrary, our predictions are aligned with the policy recommendations of
(Barr and Diamond, 2008, ch. 15), arguing against reforming the pension system in
the direction of pre-funded individual accounts. They argue that (i) although a prefunded system may induce higher savings (as it does in our model), this objective
does not seem valuable for China; (ii) a pre-funded asset-based system is likely to
lead to either low pension returns or high risk due to the large imperfections of the
Chinese financial system; and (iii) introducing a funded system would benefit future
generations of workers at the expense of today’s workers who are relatively poor and
subject to great economic uncertainty.
Our results hinge on two key features of China that are equilibrium outcomes in
our model: a high wage growth and a low rate of return on savings.3 If we lower the
wage growth to an average of 2% per year (a conventional wage growth for mature
economies), the main results are reversed: the planner who discounts the future at
an annual 0.5% would prefer a FF reform, or alternatively the immediate implementation of the draconian sustainable reform, over a PAYGO. Thus, our analysis
illustrates a general point that applies to fast-growing emerging economies. Even for
economies that are dynamically efficient, the combination of (i) a prolonged period
of high wage growth and (ii) a low return to savings to large financial imperfections
makes it possible to run a relatively generous pension system over the transition
without imposing a large burden to future generations.
The current pension system of China covers only about 60% of urban workers.
We analyze the welfare effect of making the system universal, extending its coverage
to all rural and urban workers. This issue is topical for various reasons. First, the
incidence of old-age poverty is especially severe in rural areas, and internal migration is likely to make the problem even more severe in the coming years. Second,
the government of China is currently introducing some form of rural pensions. The
recurrent question is to what extent this is affordable, and how generous rural pensions can be, since almost half of today’s population lives in rural areas, and these
workers have not contributed to the system thus far. We find that extending the
coverage of the pension system to rural workers would be relatively inexpensive,
even though full benefits were paid to workers who never contributed to the system.
As expected, this change would trigger large welfare gains for the poorest part of
the Chinese population. The cost is small, since (i) benefits are linked to local wages
3 Different from us, Feldstein (1999) assumes that the Chinese government has access to a risk-free annual
rate of return on the pension fund of 12%. Unsurprisingly, he finds that a fully funded system that collects
pension contributions and invests these funds at such a remarkable rate of return will dominate a PAYGO
pension system that implicitly delivers the same rate of return as aggregate wage growth.
4
and rural wages are low; and (ii) the rural population is shrinking.
The paper is structured as follows. Section II outlines the detailed demographic
model. Section III lays out a calibrated partial equilibrium version of Au-Ko that
incorporates the main features of the Chinese pension system. In this section, we assume exogenous paths for wages and interest rate. Section IV quantifies the effects of
the alternative pension reforms. Section V checks the sensitivity of our main findings
with respect to the key assumptions about structural features of the model economy.
Section VI provides a full general equilibrium model of the Chinese economy based
on Song, Storesletten and Zilibotti (2011), where the wage and interest rate path
assumed in section III are equilibrium outcomes. The model allows us to consider
reforms that influence the economic transition. Section VII concludes. Three appendixes (Appendixes A, B and C) contain some technical material, a description
of the Chinese pension system, and additional figures.
II.
Demographic Model
Throughout the 1950s and 1960s, the total fertility rate (henceforth, TFR) of
China was between five and six. High fertility, together with declining mortality,
brought about a rapid expansion of the total population. The 1982 census estimated
a population size of one billion, 70% higher than in the 1953 census. The view that
a booming population is a burden on the development process led the government to
introduce measures to curb fertility during the 1970s, culminating in the one-child
policy of 1978. This policy imposes severe sanctions on couples having more than
one child. The policy underwent a few reforms and is currently more lenient to rural
families and ethnic minorities. For instance, rural families are allowed a second birth
provided the first child is a girl. In some provinces, all rural families are allowed
to have a second child provided that a minimum time interval elapses between the
first and second birth. Today’s TFR is below replacement level, although there is
no uniform consensus about its exact level. Estimates based on the 2000 census and
earlier surveys in the 1990s range between 1.5 and 1.8 (e.g. Zhang and Zhao, 2006).
Recent estimates suggest a TFR of about 1.6 (see Zeng, 2007).
A.
Natural Population Projections
We consider, first, a model without rural-urban migration, which is referred to
as the natural population dynamics. We break down the population by birth place
(rural vs. urban), age, and gender. The initial population size and distribution are
matched to the adjusted 2000 census data.4 There is consensus among demographers
that birth rates have been underreported, causing a deficit of 30 to 37 million children
in the 2000 census.5 To heed this concern, we take the rural-urban population and
age-gender distribution from the 2000 census – with the subsequent National Bureau
of Statistics (NBS) revisions – and then amend this by adding the missing children
for each age group, according to the estimates of Goodkind (2004).
The initial group-specific mortality rates are also estimated from the 2000 census,
yielding a life expectancy at birth of 71.1 years, which is very close to the World
4 The 2000 census data are broadly regarded as a reliable source (see e.g. Lavely, 2001; Goodkind, 2004).
The total population was originally estimated to be 1.24 billion, later revised by the NBS to 1.27 billion (see
the Main Data Bulletin of 2000 National Population Census). The NBS also adjusted the urban-to-rural
population ratio from 36.9% to 36%.
5 See Goodkind (2004). A similar estimate is obtained by Zhang and Cui (2003), who use primary school
enrolments to back out the actual child population.
5
Development Indicator figure in the same year (71.2). Life expectancy is likely to
continue to increase as China becomes richer. Therefore, we set the mortality rates
in 2020, 2050, and 2080 to match the demographic projection by Zeng (2007) and
use linear interpolation over the intermediate periods. We assume no further change
after 2080. This implies a long-run life expectancy of 81.9 years.
The age-specific urban and rural fertility rates for 2000 and 2005 are estimated
using the 2000 census and the 2005 one-percent population survey, respectively. We
interpolate linearly the years 2001-2004, and assume age-specific fertility rates to
remain constant at the 2005 level over the period 2006-2011. This yields average
urban and rural TFR’s of 1.2 and 1.98, respectively.6 Between 2011 and 2050,
we assume age-specific fertility rates to remain constant in rural areas. This is
motivated by the observation that, according to the current legislation, a growing
share of urban couples (in particular, those in which each spouse is an only child)
will be allowed to have two children. In addition, some provinces are discussing a
relaxation of the current rule, that would allow even urban couples in which only
one spouse is an only child to have two children. Zeng (2007) estimates that such a
policy would increase the urban TFR from 1.2 to 1.8 (second scenario Zeng, 2007).
Accordingly, we assume that the TFR increases to 1.8 in 2012 and then remains
constant until 2050.
A long-run TFR of 1.8 implies an ever-shrinking population. We follow the United
Nations population forecasts and assume that in the long run the population will
be stable. This requires that the TFR converges to 2.078, which is the reproduction
rate in our model, in the long run. In order to smooth the demographic change, we
assume that both rural and urban fertility rates start growing in 2051, and we use
a linear interpolation of the TFRs for the years 2051-2099. Since long-run forecasts
are subject to large uncertainty, we also consider an alternative scenario with lower
fertility.
B.
Rural-Urban Migration
Rural-urban migration has been a prominent feature of the Chinese economy since
the 1990s. There are two categories of rural-urban migrants. The first category is all
individuals who physically move from rural to urban areas. It includes both people
who change their registered permanent residence (i.e., hukou workers) and people
who reside and work in urban areas but retain an official residence in a rural area
(non-hukou urban workers).7 The second category is all individuals who do not
move but whose place of registered residence switches from being classified as rural
into being classified as urban.8 We define the sum of the two categories as the net
migration flow (NMF).
6 The acute gender imbalance is taken into account in our model. However, demographers view it as
unlikely that such imbalance will persist at the current high levels. Following Zeng (2007), we assume that
the urban gender ratio will decline linearly from 1.145 to 1.05 from 2000 to 2030, and that the rural gender
imbalance falls from 1.19 to 1.06 over the same time interval. No change is assumed thereafter. Our results
are robust to plausible changes in the gender imbalance.
7 There are important differences across these two subcategories. Most non resident workers are currently
not covered by any form of urban social insurance including pensions. However, some relaxation of the
system has occurred in recent years. The system underwent some reforms in 2005, and in 2006 the central
government abolished the hukou requirement for civil servants (Chan and Buckingham, 2008). Since there
are no reliable estimates of the number of non-hukou workers, and in addition there is uncertainty about how
the legislation will evolve in future years, we decided not to distinguish explicitly between the two categories
of migrants in the model. This assumption is of importance with regard to the coverage of different types
of workers in the Chinese pension system. We return to this discussion below.
8 This was a sizeable group in the 1990s: according to China Civil Affairs Statistical Yearbooks, a total
of 8,439 new towns were established from 1990 to 2000 and 44 million rural citizens became urban citizens
6
We propose a simple model of migration where the age- and gender-specific emigration rates are fixed over time. Although emigration rates are likely to respond
to the urban-rural wage gap, pension and health care entitlements for migrants, the
rural old-age dependency ratio, and so on, we will abstract from this and maintain
that the demographic development only depends on the age distribution of rural
workers. It is generally difficult, even for developed countries, to predict the internal migration patterns (see e.g. Kaplan and Schulhofer-Wohl, 2012). In China,
pervasive legal and administrative regulations compound this problem.
We start by estimating the NMF and its associated distribution across age and
gender. This estimation is the backbone of our projection of migration and the
implied rural and urban population dynamics. We use the 2000 census to construct
a projection of the natural rural and urban population until 2005 based on the
method described in section II.A. We can then estimate the NMF and its distribution
across age groups by taking the difference between the 2005 projection of the natural
population and the realized population distribution according to the 2005 survey.9
The technical details of the estimation can be found in Appendix A.
According to our estimates, the overall NMF between 2000 and 2005 was 91 million, corresponding to 11.1% of the rural population in 2000.10 Survey data show
that the urban population grows at an annual 4.1% rate between 2000 and 2005.
Hence, 89% of the Chinese urban population growth during those years appears to
be accounted for by rural-urban migration. Our estimate implies an annual flow of
18.3 million migrants between 2001 to 2005, equal to an annual 2.3% of the rural
population. This figure is in line with estimates of earlier studies. For instance,
Hu (2003) estimates an annual flow between 17.5 and 19.5 million in the period
1996–2000.
The estimated age-gender-specific migration rates are shown in Figure 1. Both
the female and male migration rates peak at age fifteen, with 16.8% for females and
13.3% for males. The migration rate falls gradually at later ages, remaining above
1% until age thirty-nine for females and until age forty for males. Migration becomes
negligible after age forty. To incorporate rural-urban migration in our population
projection, we make two assumptions. First, the age-gender-specific migration rates
remain constant after 2005 at the level of our estimates for the period 2000–2005.
Second, once the migrants have moved to an urban area, their fertility and mortality
rates are assumed to be the same as those of urban residents.
Figure 2 shows the resulting projected population dynamics (solid lines). For
comparison, we also plot the natural population dynamics (i.e., the population model
without migration [dotted lines]). The rural population declines throughout the
whole period. The urban population share increases from 50% in 2011 to 80% in 2050
(Hu, 2003). However, the importance of reclassified areas has declined after 2000. Only 24 prefectures were
reclassified as prefecture-level cities in 2000-2009, while 88 prefectures were reclassified in 1991-2000.
9 Our method is related to Johnson (2003), who also exploits natural population growth rates. Our work
is different from Johnson’s in three respects. First, his focus is on migration across provinces, whereas we
estimate rural-urban migration. Second, Johnson only estimates the total migration flow, whereas we obtain
a full age-gender structure of migration. Finally, our estimation takes care of measurement error in the
census and survey (see discussion above), which were not considered in previous studies.
10 There are a number of inconsistencies across censuses and surveys. Notable examples include changes
in the definition of city population and urban area (see e.g. Zhou and Ma, 2003; Duan and Sun, 2006). Such
inconsistencies could potentially bias our estimates. In particular, the definition of urban population in the
2005 survey is inconsistent with that in the 2000 census. In the 2000 census, urban population refers to the
resident population (changzhu renkou) of the place of enumeration who had resided there for at least six
months on census day. The minimum requirement was removed in the 2005 survey. Therefore, relative to
the 2005 survey definition, rural population tends to be over-counted in the 2000 census. This tends to bias
our NMF estimates downward.
7
16
Emigration Rates from Rural Areas by Age and Gender, as a Share of Each Cohort
14
Emigration Rate (Percent)
12
10
8
Males
6
Females
4
2
0
−2
10
15
20
25
30
Age
35
40
45
50
Figure 1: The figure shows rural-urban migration rates by age and gender as a share of each cohort. The
estimates are smoothed by five-year moving averages.
and to over 90% in 2100. In absolute terms, the urban population increases from 450
million in 2000 to its long-run 1.2 billion level in 2050. Between 2050 and 2100 there
are two opposite forces that tend to stabilize the urban population: on the one hand,
fertility is below replacement in urban areas until 2100; on the other hand, there is
still sizeable immigration from rural areas. In contrast, had there been no migration,
the urban population would have already started declining in 2008. Figure 3 plots
the old-age dependency ratio (i.e., the number of retirees as percentage of individuals
in working age [18-60]) broken down by rural and urban areas (solid lines).11 We also
plot, for contrast, the old-age dependency ratio in the no migration counterfactual
(dashed lines). Rural-urban migration is very important for the projection. The
projected urban dependency ratio is 50% in 2050, but it would be as high as 80% in
the no migration counterfactual. This is an important statistic, since the Chinese
pension system only covers urban workers, so its sustainability hinges on the urban
old-age dependency ratio.
III.
A Partial Equilibrium Model
In this section, we construct and calibrate a multiperiod OLG model à la Auerbach
and Kotlikoffhor (1987), consistent with the demographic model of section II. Then,
after feeding an exogenous wage growth process into it, we use the model to assess
the welfare effects of alternative sustainable pension reforms. In section VI we show
that the assumed wage process is the equilibrium outcome of a calibrated dynamic
general-equilibrium model with credit market imperfections close in spirit to Song,
Storesletten and Zilibotti (2011).
11 In China, the official retirement age is 55 for females and 60 for males. In the rest of the paper, we
ignore this distinction and assume that all individuals retire at age 60, anticipating that the age of retirement
is likely to increase in the near future. We also consider the effect of changes in the retirement age.
8
Population Dynamics of China
1.5
Total
Population Size (Billions)
Urban
1
0.5
Rural
0
2000
2010
2020
2030
2040
2050
Time
2060
2070
2080
2090
2100
Figure 2: The figure shows the projected population dynamics for 2000-2100 (solid lines) broken down by
rural and urban population. The dashed lines show the corresponding natural population dynamics (i.e.,
the counterfactual projection under a zero urban-rural migration scenario).
A.
Households
The model economy is populated by a sequence of overlapping generations of
agents. Each agent lives up to J − JC years and has an unconditional probability
of surviving until age j equal to sj . During their first JC − 1 years (childhood),
agents are economically inactive, make no choices, and gain no utility. Preferences
are defined over consumption and leisure and are represented by a standard lifetime
utility function,
J
Ut =
sj β j u (ct+j , ht+j ) ,
j=0
where c is consumption and h is labor supply. Here, t denotes the period in which the
agent becomes adult (i.e., economically active). Thus, Ut is the discounted utility
of an agent born in period t − JC .
Workers are active until at age JW . For simplicity, we abstract from an endogenous choice of retirement. Incorporating endogenous retirement would require a
more sophisticated model of labor supply, including non-convexities in labor market
participation and declining health and productivity in old age (see e.g. Rogerson and
Wallenius, 2009). Since China has a mandatory retirement policy, the assumption
of exogenous retirement seems reasonable. After retirement, agents receive pension
benefits until death. Wages are subject to proportional taxes. Adult workers and
retirees can borrow and deposit their savings with banks paying a gross annual interest rate R. A perfect annuity market allows agents to insure against uncertainty
about the time of death.
9
Projected Old−age Dependency Ratios
2
1.8
Ratio Population 60+ / Population 18−59
1.6
1.4
Rural
1.2
1
0.8
0.6
0.4
Urban
0.2
0
2000
2010
2020
2030
2040
2050
Time
2060
2070
2080
2090
2100
Figure 3: The figure shows the projected old-age dependency ratios, defined as the ratio of population
60+ over population 18-59, for 2000-2100 (solid lines). Blue (black) lines denote urban (rural) dependency
ratios. The dashed lines show the corresponding ratios under the natural population dynamics (i.e., under
the zero migration counterfactual).
Agents maximize Ut , subject to a lifetime budget constraint,
JW
J
sj
sj
c
=
(1 − τt+j ) ζj ηt wt+j ht,t+j +
t+j
j
R
Rj
j=0
j=0
J
j=JW +1
sj
bt,t+j ,
Rj
where bt,t+j denotes the pension accruing in period t + j to a person who became
adult in period t, wt+j is the wage rate per efficiency unit at t + j, ηt denotes the
human capital specific to the cohort turning adult in t (we abstract from withincohort differences in human capital across workers), and ζj is the efficiency units per
hour worked for a worker with j years of experience, which captures the experiencewage profile.
The government runs a pension system financed by a social security tax levied
on labor income and by an initial endowment, A0 . The government intertemporal
budget constraint yields


JW
∞
J
(1)
R−t 
Nt−j,t bt−j,t − τt
Nt−j,t ζj ηt−j wt ht−j,t  ≤ A0 ,
t=0
j=0
j=JW +1
where Nt−j,t is the number (measure) of agents in period t who became active in
period t − j.
B.
The Pension System
The model pension system replicates the main features of China’s pension system
(see Appendix B for a more detailed description of the actual system). The current
10
system was originally introduced in 1986 and underwent a major reform in 1997.
Before 1986, urban firms (which were almost entirely state owned at that time)
were responsible for paying pensions to their former employees. This enterprisebased system became untenable in a market economy where firms can go bankrupt
and workers can change jobs. The 1986 reform introduced a defined benefits system
whose administration was assigned to municipalities. The new system came under financial distress, mostly due to firms evading their obligations to pay pension
contributions for their workers.
The subsequent 1997 reform tried to make the system sustainable by reducing the
replacement rates for future retirees and by enforcing social security contributions
more strictly. The 1997 system has two tiers (plus a voluntary third tier). The
first is a standard transfer-based basic pension system with resource pooling at
the provincial level. The second is an individual accounts system. However, as
documented by (Sin, 2005, p.2), “the individual accounts are essentially ‘empty
accounts’ since most of the cash flow surplus has been diverted to supplement the
cash flow deficits of the social pooling account.”Due to its low capitalization, the
system can be viewed as broadly transfer-based, although it permits, as does the US
Social Security system, the accumulation of a trust fund to smooth the aging of the
population. Since the individual accounts are largely notional, we decided to ignore
any distinction between the different pension pillars in our analysis.
We model the pension system as a defined benefits plan, subject to the intertemporal budget constraint, (1). Appendix B shows explicitly how the institutional
details are mapped into the simple model. In line with the actual Chinese system,
pensions are partly indexed to wage growth. We approximate the benefit rule by a
linear combination of the average earnings of the beneficiary at the time of retirement and the current wage of workers about to retire, with weights 60% and 40%,
respectively. More formally, the pension received at period t + j by an agent who
worked until period t + JW (and who became adult in period t) is
(2)
bt,t+j = qt+JW · (0.6 · ȳt+JW + 0.4 · ȳt+j−1 ) ,
where qt denotes the replacement rate in period t and ȳt is the average pre-tax labor
earnings for workers in period t:
ȳt ≡
wt
Jw
j=0 Nt−j,t ηt−j ζj
Jw
j=0 Nt−j,t
ht−j,t
.
In line with the 1997 reform (see e.g. Sin, 2005), we assume that pensioners retiring
before 1997 continued to earn a 78% replacement rate throughout their retirement.
Moreover, those retiring between 1997 and 2011 are entitled to a 60% replacement
ratio.
We assume a constant social security tax (τ ) equal to 20%, in line with the empirical evidence.12 The tax and the benefit rule do not guarantee that the system is
financially viable. In fact, we will show that, given our forecasted wage process and
demographic dynamics, the current system is not sustainable, so long-run budget
balance requires either tax hikes or benefit reductions. In this paper we focus mainly
12 The statutory contribution rate including both basic pensions and individual accounts is 28%. However,
there is evidence that a significant share of the contributions is evaded, even for workers who formally
participated in the system. See the appendix for details.
11
on reducing benefits. As a benchmark (labeled the benchmark reform), we assume
that in 2012 the replacement rate is lowered permanently to a new level to satisfy
the intertemporal budget constraint, (1).
The current pension system of China covers only a fraction of the urban workers.
The coverage rate has grown from about 40% in 1998 to 57% in 2009. In the baseline
model, we assume a constant coverage rate of 60%. The coverage rate of migrant
workers is a key issue. Since we do not have direct information about their coverage,
we decided to simply assume that rural immigrants get the same coverage rate as
urban workers. This seems a reasonable compromise between two considerations.
On the one hand, the coverage of migrant workers (especially low-skill non-hukou
workers) is lower than that of non-migrant urban residents; on the other hand, the
total coverage has been growing since 1997.13
We then consider a set of alternative reforms. First, we assume that the current
rules are kept in place until period T (where T > 2011), in the sense that the current
replacement rate (qt = 60%) applies for those who retire until period T . Thereafter,
the replacement rates are adjusted permanently so as to satisfy (1). Clearly, the
size of the adjustment depends on T : since the system is currently unsustainable,
a delay requires a larger subsequent adjustment. We label such a scenario delayed
reform.
Next, we consider a reform that eliminates the transfer-based system introducing,
a mandatory saving-based pension system in 2012. In our stylized model such a
FF system is identical to a world with no pension system because agents are fully
rational and not subject to borrowing constraints or time inconsistency in their
saving decisions. In the FF reform scenario, the pension system is abolished in
2012. However, the government does not default on its outstanding liabilities: those
who are already retired receive a lump-sum transfer equal to the present value of
the benefits they would have received under the benchmark reform. Moreover, those
still working in 2012 are compensated for their accumulated pension rights, scaled by
the number of years they have contributed to the system. To cover these lump-sum
transfers, the government issues debt. In order to service this debt, the government
introduces a new permanent tax on labor earnings, which replaces the (higher)
former social security tax.
Next, we consider switching to a pure PAYGO reform system where the tax rate
τ is kept constant at 20% and the pension budget has to be balanced each period.
So, the benefit rate is endogenously determined by the tax revenue (which is, in
turn, affected by the demographic structure and endogenous labor supply). Finally,
we consider two reforms that extend the coverage of the pension system to rural
workers. The moderate rural reform scenario offers a 20% replacement rate to rural
retirees financed by a 6% social security tax on rural workers. Such a rural pension
is similar to a scheme started recently by the government on a limited scale (see
Appendix B for details). The radical rural reform scenario introduces a universal
pension system with the same benefits and taxes in rural and urban areas.
C.
Calibration
One period is defined as a year and agents can live up to 100 years (J = 100).
The demographic process (mortality, migration, and fertility) is described in section
13 According to a recent document issued by the National Population and Family Planning Commission,
28% of migrant workers are covered by the pension system (Table 5-1, 2010 Compilation of Research Findings
on the National Floating Population).
12
II. Agents become adult (i.e., economically active) at age JC = 23 and retire at
age 60, which is the male retirement age in China (so JW = 59). Hence, workers
retire after 37 years of work. We set the age-wage profile {ζj }59
j=23 equal to the
one estimated by Song and Yang (2010) for Chinese urban workers. This implies an
average return to experience of 0.5%. In this section of the paper, we take the hourly
wage rate as exogenous. The assumed dynamics of urban wages per effective unit
of labor is shown in Figure 4: Hourly wages (conditional on human capital) grow
at approximately 5.7% between 2000 and 2011, 5.1% between 2011 and 2030, and
2.7% between 2030 and 2050. In the long run, wages are assumed to grow at 2% per
year, in line with wage growth in the United States over the last century. In section
VI, we show that the assumed wage rate dynamics of Figure 4 is the equilibrium
outcome of a calibrated version of the model of Song, Storesletten and Zilibotti
(2011) There has been substantial human capital accumulation in China over the
Labor Earnings Conditional on Human Capital
Labor Earnings (Log Scale)
1600
800
400
200
100
2000
2010
2020
2030
2040
2050
Time
2060
2070
2080
2090
2100
Figure 4: The figure shows the projected hourly wage rate per unit of human capital in urban areas,
normalized to 100 in 2000. The process is the endogenous outcome of the general equilibrium model of
section VI.
last two decades. To incorporate this aspect, we assume that each generation has a
cohort-specific education level, which is matched to the average years of education
by cohort according to Barro and Lee (2010) (see Figure C-1 in Appendix C). The
values for cohorts born after 1990 are extrapolated linearly, assuming that the growth
in the years of schooling ceases in year 2000 when it reaches an average of 12 years,
which is the current level for the US. We assume an annual return of 10% per year
of education.14 Since younger cohorts have more years of education, wage growth
across cohorts will exceed that shown in Figure 4. However, the education level for
an individual remains constant over his/her worklife, so Figure 4 is the relevant time
path for the individual wage growth.
14 Zhang et al. (2005) estimated returns to education in urban areas of six provinces from 1988 to 2001.
The average returns were 10.3% in 2001.
13
The rate of return on capital is very large in China (see e.g. Bai, Hsieh and Qian,
2006). However, these high rates of return appear to have been inaccessible to the
government and to the vast majority of workers and retirees. Indeed, in addition to
housing and consumer durables, bank deposits are the main asset held by Chinese
households in their portfolio. For example, in 2002 more than 68% of households’
financial assets were held in terms of bank deposits and bonds, and for the median
decile of households this share is 75% (source: Chinese Household Income Project,
2002). Moreover, aggregate household deposits in Chinese banks amounted to 76.6%
of GDP in 2009 (source: National Bureau of Statistics of China, 2010). High rates
of return on capital do not appear to have been available to the government, either.
Its portfolio consists mainly of low-yield bonds denominated in foreign currency and
equity in state-owned enterprises, whose rate of return is lower than the rate of
return to private firms (see Dollar and Wei, 2007).
Building on Song, Storesletten and Zilibotti (2011), the model of section VI provides an explanation – based on large credit market imperfections – for why neither
the government nor the workers have access to the high rates of return of private
firms. In this section, we simply assume that the annual rate of return for private and
government savings is R = 1.025. This rate is slightly higher than the empirical oneyear real deposit rate in Chinese banks, which was 1.75% during 1998-2005 (nominal
deposit rate minus CPI inflation). The choice of 2.5% per year is, in our view, a
conservative benchmark and reflects the possibility that some households have access to savings instruments that yield higher returns. Appendix B documents that
it is also in line with the returns to government pension funds. Moreover, this rate
of return seems like a reasonable long-run benchmark as China becomes a developed
country.15
Consider, finally, preference parameters: the discount factor is set to β = 1.0175
to capture the large private savings in China. This is slightly higher than the value
(1.011) that Hurd (1989) estimated for the United States. As a robustness check,
we also consider an alternative economy where β is lower for all people born after
2012 (see section V). In section VI we document that with β = 1.0175 the model
economy matches China’s average aggregate saving rate during 2000-2010.
We assume that preferences are represented by the following standard utility function:
1
u (c, h) = log c − h1+ φ ,
where φ is the Frisch elasticity of labor supply. We set φ = 0.5, in line with standard
estimates in labor economics (Keane, 2011). Note that both the social security tax
and pensions in old age distort labor supply.
Finally, we obtain the initial distribution of wealth in year 2000 by assuming that
all agents alive in 1992 had zero wealth (since China’s market reforms started in
1992). Given the 1992 distribution of wealth for workers and retirees, we simulate
the model over the 1992-2000 period, assuming an annual wage growth of 5.7%,
excluding human capital growth. The distribution of wealth in 2000 is then obtained
endogenously. The initial government wealth in 2000 is set to 71% of GDP. As we
explain in detail below, this is consistent with the observed foreign surplus in year
2000 given the calibration of the general equilibrium model in section VI.
15 Assuming a very low R would also imply that the rate of return is lower than the growth rate of the
economy, implying dynamic inefficiency. In such a scenario, there would be no need for a pension reform
due to a well-understood mechanism (cf. Abel et al., 1989).
14
IV.
Results
Under our calibration of the model, the current pension system is not sustainable.
In other words, the intertemporal budget constraint, (1), would not be satisfied if
the current rules were to remain in place forever. For the intertemporal budget
constraint to hold, it is necessary either to reduce pension benefits or to increase
contributions.
A.
The benchmark reform
We define as the benchmark reform a pension scheme such that: (i) the existing
rules apply to all cohorts retiring earlier than 2012; (ii) the social security tax is set to
a constant τ = 20% for all cohorts; and (iii) the replacement rate q, which applies to
all individuals retiring after 2011, is set to the highest constant level consistent with
the intertemporal budget constraint, (1). All households are assumed to anticipate
the benchmark reform.16
The benchmark reform entails a large reduction in the replacement rate, from
60% to 40%. Namely, pensions must be cut by a third in order for the system to be
financially sustainable. Such an adjustment is consistent with the existing estimates
of the World Bank (see Sin, 2005, p. 30). Alternatively, if one were to keep the
replacement ratio constant at the initial 60% and to increase taxes permanently so
as to satisfy (1), then τ should increase from 20% to 30.1% as of year 2012. Figure 5
shows the evolution of the replacement rate by cohort under the benchmark reform
(panel (a), dashed line). The replacement rate is 78% until 1997 and then falls
to 60%. Under the benchmark reform, it falls further to 40% in 2012, remaining
constant thereafter. Panel (b) (dashed line) shows that such a reform implies that the
pension system runs a surplus until 2051. The government builds up a government
trust fund amounting to 261% of urban labor earnings by 2080 (panel (c), dashed
line). The interests earned by the trust fund are used to finance the pension system
deficit after 2051.17
B.
Alternative reforms
Having established that a large adjustment is necessary to balance the pension
system, we address the question of whether the reform should be implemented urgently, or whether it could be deferred. In addition, we consider two more radical
alternative reforms: a move to a FF, pure contribution-based system, and a move
in the opposite direction to a pure PAYGO system.
We compare the welfare effects of each alternative reform by measuring, for each
cohort, the equivalent consumption variation of each alternative reform relative to
the benchmark reform. Namely, we calculate what (percentage) change in lifetime
consumption would make agents in each cohort indifferent between the benchmark
16 When we consider alternative policy reforms below, we introduce them as “surprises” (i.e., agents
expect the benchmark reform, but then, unexpectedly, a different reform occurs). After the surprise, perfect
foresight is assumed. This assumption is not essential. The main results of this section are not sensitive
to different assumptions, such as assuming that all reforms (including the benchmark reform) come as a
surprise, or assuming that all reforms are perfectly anticipated.
17 Note that in panel c the government net wealth (i.e., minus the debt) is falling sharply between 2000
and 2020 when expressed as a share of urban earnings, even though the government is running a surplus.
This is because urban earnings are rising very rapidly due to both high wage growth and growth in the
number of urban workers.
15
Panel a: Replacement Rate by Year of Retirement
0.8
0.6
0.4
0.2
1960
1980
2000
2020
2040
2060
2080
2100
Time
Panel b: Tax Revenue and Pension Expenditures as Shares of Urban Earnings
0.14
0.12
Tax revenue
0.1
Expenditures, Delayed Reform
0.08
0.06
0.04
2000
Expenditures, Benchmark
2010
2020
2030
2040
2050
2060
2070
2080
2090
Time
Panel c: Government Debt as a Share of Urban Earnings
2100
2110
2100
2110
−1.5
Delayed Reform
−2
Benchmark
−2.5
−3
2000
2010
2020
2030
2040
2050
2060
Time
2070
2080
2090
Figure 5: Panel (a) shows the replacement rate qt for the benchmark reform (dashed line) versus the
case when the reform is delayed until 2040. Panel (b) shows tax revenue (blue) and expenditures (black),
expressed as a share of aggregate urban labor income (benchmark reform is dashed and the delay-until-2040
is solid). Panel (c) shows the evolution of government debt, expressed as a share of aggregate urban labor
income (benchmark reform is dashed and the delay-until-2040 is solid). Negative values indicate surplus.
and the alternative reform.18 We also aggregate the welfare effects of different
cohorts by assuming a social welfare function based on a utilitarian criterion, where
the weight of the future generation decays at a constant rate φ. More formally, the
planner’s welfare function (evaluated in year 2012) is given by
(3)
U=
∞
t=1935
t
φ Nt,t
J
β j u (ct,t+j , ht,t+j ) .
j=0
Then, the equivalent variation is given by the value ω solving
(4)
∞
∞
J
J
t
j
BEN CH
BEN CH
t
φ Nt,t
β u (1 + ω) ct,t+j
, ht,t+j
φ Nt,t
β j u c∗t,t+j , h∗t,t+j ,
=
t=1935
j=0
t=1923
j=0
where superscripts BENCH stand for the allocation in the benchmark reform and
asterisks stand for the allocation in the alternative reform.19
The planner experiences a welfare gain (loss) from the alternative allocation whenever ω > 0 (ω < 0). We shall consider two particular values of the intergenerational
discount factor, φ. First, φ = R, that is, the planner discounts future utilities at
the market interest rate, as suggested, for example, by Nordhaus (2007). We label
such a planner as the high-discount planner. Second, φ = R/ (1 + g) , where g is the
18 Note that we measure welfare effects relative to increases in lifetime consumption even for people who
are alive in 2012. This approach makes it easier to compare welfare effects across generations.
19 Note that we sum over agents alive or yet unborn in 2012. The oldest person alive became an adult in
1935, which is why the summations over cohorts indexed by t start from 1935.
16
long-run wage growth rate (recall that in our calibration, R = 1.025 and g = 0.02).
Such a lower intergenerational discount rate is an interesting benchmark, since it
implies that the planner would not want to implement any intergenerational redistribution in the steady state. We label a planner endowed with such preferences as
the low-discount planner.
Delayed reform
We start by evaluating the welfare effects of delaying the reform. Namely, we
assume that the current replacement rate remains in place until some future date T ,
when a reform similar to the benchmark reform is conducted (i.e., the system provides a lower replacement rate, which remains constant forever). A delay has two
main effects: on the one hand, the generations retiring shortly after 2012 receive
higher pensions, which increase their welfare. On the other hand, the fund accumulates a lower surplus between 2012 and the time of the reform, making necessary an
even larger reduction of the replacement rate thereafter. Thus, the delay shifts the
burden of the adjustment from the current (poorer) generations to (richer) future
generations.
Figure 5 describes the positive effects of delaying the reform until 2040. Panel (a)
shows that the post-reform replacement rate now falls to 38.4%, which is only 1.6
percentage points lower than the replacement rate granted by the benchmark reform.
Panel (b) shows that the pension expenditure is higher than in the benchmark reform
until 2066. Moreover, already in 2048 the system is running deficits. As a result,
the government accumulates a smaller trust fund during the years in which the
dependency ratio is low. The reason of small differences in the replacement rate is
threefold. First, the urban working population continues to grow until 2040, due to
internal migration. Second, wage growth is high between 2012 and 2040. Third, the
trust fund earns an interest rate of only 2.5%, well below the average wage growth.
The second and third factors, which are exogenous in this section, will be derived
as the endogenous outcome of a calibrated general equilibrium model with credit
market imperfections in section VI.
Consider, next, deferring the reform until 2100 (see Figure C-2 in Appendix C). In
this case, the pension system starts running a deficit as of year 2043. The government
debt reaches 200% of the aggregate urban labor earnings in 2094. Consequently,
the replacement rate must fall to 29.7% in 2100. Figure 6 shows the equivalent
variations, broken down by the year of retirement for each cohort. Panel (a) shows
the case in which the reform is delayed until 2040. The consumption equivalent
gains for agents retiring between 2012 and 2039 are large: on average over 17% of
their lifetime consumption! The main reason is that delaying the reform enables the
transition generation to share the gains from high wage growth after 2012, to which
pension payments are (partially) indexed. The welfare gain declines over the year
of cohort retirement, since wage growth slows down. Yet, the gains of all cohorts
affected are large, being bounded from below by the 15.5% gains of the generation
retiring in 2039. On the contrary, all generations retiring after 2039 lose, though
their welfare losses are quantitatively small, being less than 1.1% of their lifetime
consumption. The difference between the large welfare gains accruing to the first 29
cohorts and the small losses suffered by later cohorts is stark. A similar trade-off can
be observed in panel (b) for the case in which the reform is delayed until 2100. In
this case, the losses accruing to the future generations are larger: all agents retiring
after 2100 suffer a welfare loss of 4.6%.
17
Welfare Gain (Equiv. Variation) by Year of Retirement
Welfare Gain ω (in Percent)
30
Delayed Reform Until 2040
30
20
20
10
10
0
0
−10
−10
−20
2000
2020
2040
2060
2080
2100
2020
Fully Funded Reform
30
2040
2060
2080
2100
PAYGO Reform
60
20
40
10
20
0
0
−10
−20
2000
−20
2000
Delayed Reform Until 2100
2020
2040
2060
2080
2100
−20
2000
2020
2040
2060
2080
2100
Year of Retirement
Figure 6: The four panels show welfare gains of alternative reforms relative to the benchmark reform for
each cohort. The gains (ω) are expressed as percentage increases in consumption (see eq. 4).
Figure 7 shows the welfare gains/losses of delaying the reform until year T , according to the utilitarian social welfare function. The figure displays two curves: in
the upper curve, we have the consumption equivalent variation of the high-discount
planner, while in the lower curve we have that of the low-discount planner.
Consider, first, delaying the reform until 2040. The delayed reform yields ω = 5%
for the high-discount planner (i.e., the delayed reform is equivalent to a permanent
5% increase in consumption in the benchmark allocation). The gain is partly due
to the fact that future generations are far richer and, hence, have a lower marginal
utility of consumption. For instance, in the benchmark reform scenario, the average
pension received by an agent retiring in 2050 is 5.28 times larger than that of an
agent retiring in 2012. Thus, delaying the reform has a strong equalizing effect
that increases the utilitarian planner’s utility. The welfare gain of the low-discount
planner remains positive, albeit smaller, ω = 0.8%.
The figure also shows that the high-discount planner would maximize her welfare
gain by a long delay of the reform (the curve is uniformly increasing in the range
shown in the figure. In contrast, the low-discount planner would maximize her
welfare gain by delaying the reform until year 2049.
Fully Funded Reform
Consider, next, switching to a FF system (i.e., a pure contribution-based pension
system featuring no intergenerational transfers, where agents are forced to save for
their old age in a fund that has access to the same rate of return as that of private
savers). As long as agents are rational and have time-consistent preferences, and
mandatory savings do not exceed the savings that agents would make privately in
the absence of a pension system, a FF system is equivalent to no pension system.
However, switching to a FF system does not cancel the outstanding liabilities (i.e.,
18
Welfare Gains of Delaying the Reform (Utilitarian Planner)
8
Welfare Gain ω (in Percent)
7
6
High Discount Rate
5
4
3
2
Low Discount Rate
1
2020
2030
2040
2050
2060
2070
Period T of Reform Implementation
2080
2090
2100
Figure 7: The figure shows the consumption equivalent gain/loss accruing to a high-discount planner
(solid line) and to a low-discount planner (dashed line) of delaying the reform until time T relative to the
benchmark reform. When ω > 0, the planner strictly prefers the delayed reform over the benchmark reform.
payments to current retirees and entitlements of workers who have already contributed to the system). We will therefore design a reform such that the government
does not default on existing claims. In particular, we assume that all workers and
retirees who have contributed to the pension system are refunded the present value
of the pension rights they have accumulated.20 Since the social security tax is abolished, the existing liabilities are financed by issuing government debt, which in turn
must be serviced by a new tax. This scheme is similar to that adopted in the 1981
pension reform of Chile. Figure 8 shows the outcome of this reform. The old system
is terminated in 2011, but people with accumulated pension rights are compensated
as discussed above. To finance such a pension buy out scheme, government debt
must increase to over 87% of total labor earnings in 2011. A permanent 0.3% annual tax is needed to service such a debt. The government debt first declines as
a share of total labor earnings due to high wage growth in that period, and then
stabilizes at a level about 30% of labor earnings around 2040. Agents born after
2040 live in a low-tax society with no intergenerational transfers.
Panel (c) of Figure 6 shows the welfare effects of the FF reform relative to the
benchmark. The welfare effects are now opposite to those of the delayed reforms.
The cohorts retiring between 2012 and 2058 are harmed by the FF reform relative
to the benchmark. There is no effect on earlier generations, since those are fully
compensated by assumption. The losses are also modest for cohorts retiring soon
after 2012, since these have earned almost full pension rights by 2012. However,
the losses increase for later cohorts and become as large as 11% for those retiring
20 In particular, people who have already retired are given an asset worth the present value of the pensions
according to the old rules. Since there are perfect annuity markets, this is equivalent to the pre-reform
scenario for those agents. People who are still working and have contributed to the system are compensated
in proportion to the number of years of contributions.
19
Panel a: Replacement Rate by Year of Retirement
0.8
0.6
0.4
0.2
0
1960
0.1
1980
2000
2040
2060
2080
2100
Time
Panel b: Tax Revenue and Pension Expenditures as Shares of Urban Earnings
Tax revenue
Expenditures, Benchmark
0.05
0
2000
2020
2010
2020
2030
Expenditures, FF Reform
2050
2060
2070
2080
2090
Time
Panel c: Government Debt as a Share of Urban Earnings
0
2040
2100
2110
2100
2110
FF Reform
−1
Benchmark
−2
−3
2000
2010
2020
2030
2040
2050
2060
Time
2070
2080
2090
Figure 8: The figure shows outcomes for the fully funded reform (solid lines) versus the benchmark reform
(dashed lines). Panel (a) shows the replacement rates. Panel (b) shows taxes (blue) and pension expenditures
(black) for the fully funded reform (solid lines) versus the benchmark reform (dashed lines) expressed as a
share of aggregate urban labor income. Panel (c) shows the government debt as a share of aggregate urban
labor income.
in 2030-35. For such cohorts, the system based on intergenerational transfer is
attractive, since wage growth is high during their retirement age (implying fastgrowing pensions), whereas the returns on savings are low. Losses fade away for
cohorts retiring after 2050 and turn into gains for those retiring after 2058. The
fact that generations retiring sufficiently far in the future gain is guaranteed by the
assumption that the economy is dynamically efficient. However, the long-run gains
are modest. The high-discount planner strictly prefers the benchmark over the FF
reform, the consumption equivalent discounted loss being 3.5%. In contrast, the
low-discount planner makes a 0.2% consumption equivalent gain. This small gain
arises from the labor supply adjustment triggered by the lower tax distortion. If
labor supply were inelastic, even the low-discount planner would lose by moving to
a fully funded system.
Pay-as-you-go reform
We now analyze the effect of moving to a pure PAYGO. In particular, we let
the contribution rate be fixed at τ = 20% and assume that the benefits equal the
total contributions in each year. Therefore, the pension benefits bt in period t are
20
endogenously determined by the following formula:21
bt =
τ
JW
j=0 Nt−j,t ζj ηt−j wt
J
j=JW +1 Nt−j,t
ht−j,t
.
Figure 9 shows the outcome of this reform. Panel (a) reports the pension benefits as
a fraction of the average earnings by year. Note that this notion of replacement rate
is different from that used in the previous experiments (panel a of Figures 5, 8 and
C-2); there the replacement rate was cohort specific and was computed according
to equation (2) by the year of retirement of each cohort. Until 2050, the PAYGO
reform implies larger average pensions than under the benchmark reform.
Panel (b) shows the lifetime pension as a share of the average wage in the year of
retirement, by cohort. This is also larger than in the benchmark reform until the
cohort retiring in 2044. We should note that, contrary to the previous experiments
which were neutral vis-à-vis cohorts retiring before 2012, here even earlier cohorts
benefit from the PAYGO reform, since the favorable demographic balance yields
them higher pensions than what they had been promised. This can clearly be seen
in panel (b) of figure 9 and panel (c) of figure 6. Welfare gains are very pronounced
for all cohorts retiring before 2044, especially so for those retiring in 2012 and in the
few subsequent years, who would suffer a significant pension cut in the benchmark
reform. These cohorts retire in times when the old-age dependency ratio is still very
low and therefore would benefit the most from a pure PAYGO system. On the other
hand, generations retiring after 2045 suffer a loss relative to the benchmark reform.
Due to the strong redistribution in favor of poorer early generations, the utilitarian
welfare is significantly higher under the PAYGO reform than in the benchmark
reform, for both a high- and low-discount planner. The consumption equivalent
gains relative to the benchmark reform are, respectively, 13.5% and 1.8% for urban
workers. These gains are larger than under all alternative reforms (including delayed
and FF reform). These results underline that the gains for earlier generations come
at the expense of only small losses for the future generations.
Increasing retirement age
An alternative to reducing pension benefits would be to increase the retirement
age. Our model allows us to calculate the increase in retirement age that would be
required to balance the intertemporal budget, (1), given the current social security
tax and replacement rate. We find such an increase to be equal to approximately
six years (i.e., retirement age would have to increase from 60 to 66 years without
any reduction in employment). This shows that a draconian reduction in pension
entitlements may not be necessary if the retirement age can be increased. Since our
model abstracts from an endogenous choice of retirement, we do not emphasize the
welfare effects of policies affecting retirement age (there would obviously be a large
welfare gain if the retirement age is increased exogenously).
21 Note that the pension system has accumulated some wealth before 2011. We assume that this wealth
is rebated to the workers in a similar fashion as the implicit burden of debt was shared in the fully funded
experiment. In particular, the government introduces a permanent reduction δ in the labor income tax, in
such a way that the present value of this tax subsidy equals the 2011 accumulated pension funds. In our
calibration, we obtain δ = 0.54%.
21
Panel a: Pension Payment / Labor Earnings by Year
1.5
1
PAYGO
0.5
Benchmark
0
2000
40
2010
2020
2030
2040
2050
2060
Year
2070
2080
2090
2100
2110
Panel b: Lifetime Pension / Average Labor Earnings in the Year of Retirement, by Cohort
30
PAYGO
20
10
0
Benchmark
1980
2000
2020
2040
2060
Year of Retirement
2080
2100
Figure 9: Panel (a) shows the average pension payments in year t as a share of average wages in year t
for the PAYGO (solid) and the benchmark reform (dashed line). Panel (b) shows the ratio of the lifetime
pensions (discounted to the year of retirement) to the average labor earnings just before retirement for each
cohort.
Rural Pension
The vast majority of people living in rural areas are not covered by the current
Chinese pension. In accordance with this fact, we have so far maintained the assumption that only urban workers are part of the pension system. In this section,
we consider extending the system to rural workers.
Although a rural and an urban pension system could in principle be separate
programs, we assume that there is a consolidated intertemporal budget constraint,
namely, the government can transfer funds across the rural and urban budget. This
is consistent with the observation that the modest rural pension system that China
is currently introducing is heavily underfunded (see Appendix B), suggesting that
the government implicitly anticipates a resource transfer from urban to rural areas.
The modified consolidated government budget constraint then becomes

JW
∞
r
A0 +
R−t 
ζj τt Nt−j,t wt ht−j,t + τtr Nt−j,t
wtr hrt−j,t −
(5)
t=0
J
j=JW +1
j=0

r
brt−j,t  ≥ 0,
Nt−j,t bt−j,t + Nt−j,t
where superscripts r denote variables pertaining to the rural areas, whereas urban
variables are defined, as above, without any superscript.
We assume the rural wage rate to be 54% of the urban wage in 2000, consistent
with the empirical evidence from the China Health and Nutrition Survey. The annual
22
rural wage growth is assumed to be 3.2% between 2000-2040, and 2% thereafter (see
Figure C-3 in Appendix C). This is consistent with the prediction of the general
equilibrium model outlined in section VI.
We consider two experiments. In the first (low-scale reform), we introduce a rural
pension system with rules that are different from those applying to urban areas
in 2012. This experiment mimics the rules of the new old-age programs that the
Chinese government is currently introducing for rural areas (see Appendix B). Based
on the current policies, we set the rural replacement rate (qtr ) and contribution rate
(τtr ) to 20% and 6%, respectively. These rates are assumed to remain constant
forever. Moreover, we assume that all rural inhabitants older than retirement age in
2012 are eligible for this pension. Introducing such a scheme in 2012 would worsen
the fiscal imbalance. Restoring the fiscal balance through a reform in 2012 requires
that the replacement rate of urban workers be cut to qt = 38.7%, 1.3 percentage
points lower than in the benchmark reform without rural pensions. Hence, the rural
pension implies a net transfer from urban to rural inhabitants.
A low-discount planner who only cares for urban households participating in the
pension system would incur a welfare loss of less than 0.6% from expanding the
pension system to rural inhabitants. In contrast, a low-discount planner who only
cares for rural households would incur a welfare gain of 6.5%. When weighting
rural and urban households by their respective population shares, one obtains an
aggregate welfare gain of 0.4% relative to the benchmark reform.22
The second experiment (drastic reform) consists of turning the Chinese pension
system into a universal system, pooling all Chinese workers and retirees – in both
rural and urban areas – into a system with common rules. As of 2012, all workers
contribute 20% of their wage. In addition, the system bails out all workers who
did not contribute to the system in the past. Namely, all workers are paid benefits
according to the new rule even though they had not made any contribution in the
past. Although rural and urban retirees have the same replacement rate, pension
benefits are proportional to the group-specific wages (i.e., rural [urban] wages for
rural [urban] workers). As in the benchmark reform above, the replacement rate is
adjusted in 2012 so as to satisfy the intertemporal budget constraint of the universal
pension system. Although we ignore issues with the political and administrative
feasibility of such a radical reform, this experiment provides us with an interesting
upper bound of the effect of a universal system.
The additional fiscal imbalance from turning the system into a universal one is
small: the replacement rate must be reduced to qt = 38.7% from 2012 onward,
relative to 40% in the benchmark reform. The welfare loss for urban workers participating in the system is very limited – the high-discount planner would suffer a
0.53% loss relative to the benchmark (only marginally higher than in the low-scale
reform). In contrast, the welfare gains for urban workers not participating in the
system are very large (+13.3% if evaluated by the high-discount planner). Rural
workers would also gain substantially (+6.5% if evaluated by the high-discount planner). The average effect (assessed from the standpoint of the high-discount planner
weighting equally all inhabitants) is 5%.
To understand why this reform can give so large gains with such a modest ad22 A high-discount planner who only cares for urban households participating in the pension system would
incur a welfare loss of less than 0.64% from expanding the pension system to rural inhabitants. A highdiscount planner who only cares for rural households would incur a welfare gain of 12.4%. When weighting
rural and urban households by their respective population shares, one obtains an aggregate welfare gain of
2% relative to the benchmark reform.
23
ditional fiscal burden, it is important to emphasize that (i) the earnings of rural
workers are on average much lower than those of urban workers; and (ii) the rural
population is declining rapidly over time. Both factors make pension transfers to
the rural sector relatively inexpensive. It is important to note that our calculations
ignore any cost of administering and enforcing the system. In particular, the benefit
would decrease if the enforcement of the social security tax in rural areas proves to
be more difficult than in urban areas.
V.
Sensitivity analysis
In this section, we study how the main results of the previous section depend on
key assumptions about structural features of the model economy: wage growth, population dynamics, and interest rate. For simplicity, we focus on the urban pension
system (no payments to rural workers). We refer to the calibration of the model
used in the previous section as the baseline economy.
A.
Low wage growth
First, we consider a low wage growth scenario. In particular, we assume wage
growth to be constant and equal to 2%. In this case, the benchmark reform implies
a replacement rate of 40.5%. Note that in the low wage growth economy, the present
value of the pension payments is lower than in the baseline economy, since pensions
are partially indexed to the wage growth. Thus, pensions are actually lower, in spite
of the slightly higher replacement rate.
Next, we consider the welfare effects of the alternative reforms. The top-left
panel of Figure 10 plots the welfare gains/losses of generations retiring between
2000 and 2110 in the case of a delay of the reform until 2040 (dashed line) and
2100 (continuous line). The top-center and top-right panels of Figure 10 yield the
welfare gains/losses in the case of a FF reform (center) and PAYGO (right). Recall
that gains and losses are expressed relative to the benchmark reform, and thus a
cohort gains (loses) when the curve is above (below) unity. Delaying the reform
until 2040 (2100) yields a replacement rate of 40.5% (38.4%). The welfare gains
of the earlier generations relative to the benchmark reform are significantly smaller
than in the baseline economy. For instance, if the reform is delayed until 2040 the
cohorts retiring between 2012 and 2039 experience a consumption equivalent welfare
gain ranging between 8% and 9%. The cost imposed on the future generations is
similar in magnitude to that of the baseline economy. The high-discount planner
enjoys a consumption equivalent gain of 2.4%, which is significantly lower than the
5% gain found in the baseline economy. For the low-discount planner, the gain is
almost 0. Thus, more than half of the welfare gains of delaying the reform accrue
due to the high wage growth. In the alternative of a delayed reform until 2100,
the high-discount planner enjoys a welfare gain of less than 5.6%, compared with
8.6% in the baseline economy. Moreover, the low-discount planner now prefers the
benchmark reform over a reform delayed until 2100.
As in the baseline case, the FF alternative reform harms earlier cohorts, whereas
it benefits all cohorts retiring after 2046. However, the relative losses of the earlier
cohorts are significantly smaller than in the baseline economy. For instance, the
cohort that is most negatively affected by the FF reform suffers a loss of 3.9% in
the low wage growth economy, compared to a 11.3% loss in the baseline economy.
Accordingly, the high-discount planner suffers a smaller welfare loss (0.5%) than in
24
25
20
20
60
15
15
50
10
Consumption Equivalent Gain/Loss (in Percent)
Sensitivity Analysis: Welfare Gains by Cohorts Under Different Scenarios
Low Wage Growth
25
70
Delayed Until 2040
5
5
0
0
−5
−5
−10
−10
−15
2000
2050
2100
25
20
−15
2000
25
Delayed until 2040
15
10
10
5
5
0
0
−5
−5
−10
−10
2050
2100
Fully Funded
−15
2000
30
20
PAYGO
10
0
−10
2050
2100
Low Fertility
2000
2050
2100
80
20
15
−15
2000
40
10
60
Fully Funded
40
PAYGO
20
0
2050
2100
2000
2050
2100
T (Time of Retirement)
Figure 10: The figure shows consumption equivalent gains/losses accruing to different cohorts in two
alternative scenarios. The top panels refer to the low wage growth scenario of section V.A. The bottom
panels refer to the low fertility scenario of section V.B. In each panel, the dashed red lines refer to the
welfare gains under the benchmark calibration (see section IV). The left-hand panels show the consumption
equivalent gains/losses associated with delaying the reform until 2040 (solid blue lines). The center panels
show the consumption equivalent gains/losses associated with a fully funded reform (solid blue lines). The
right-hand panels show the consumption equivalent gains/losses associated with a PAYGO reform (solid
blue lines).
the baseline economy (3.5%). Thus, about 85% of the loss accruing to the utilitarian
planner arises from the high implicit return of intergenerational transfers due to high
wage growth in the baseline economy. Interestingly, the low-discount planner would
now prefer the FF reform over any of the alternatives. She would also prefer no
delay to any of the delayed reforms.
Finally, the large welfare gains from the PAYGO alternative reform by and large
vanish. Although the high-discount planner would still prefer the PAYGO reform
to the benchmark reform, the consumption equivalent gain would be about a third
of that in the high growth scenario. Perhaps more interesting, the low-discount
planner who has no built-in preference for transfers to the earlier generations at a
given interest rate would now prefer the benchmark reform to the PAYGO reform.
Thus, the welfare ranking order of the low discount planner is: FF reform first, then
benchmark reform, and last PAYGO reform.
In summary, high wage growth magnifies the welfare gains of delaying a reform (or
of switching to PAYGO) and increases the welfare costs of a FF reform relative to the
benchmark reform. This result is not unexpected, since high wage growth increases
the implicit return of a system based on intergenerational transfers. The comparison
with a constant 2% wage growth scenario is especially revealing, since it is consistent
with the standard assumption for pension analyses of developed economies.
25
B.
Lower fertility
Our forecasts are based on the assumption that the TFR will increase to 1.8
already in 2012. This requires a reform or a lenient implementation of the current
one-child policy rules. In this section, we consider an alternative lower fertility
scenario along the lines of scenario 1 in Zeng (2007). In this case, the TFR is
assumed to be 1.6 forever, implying an ever-shrinking total population. We view
this as a lower bound to reasonable fertility forecasts. Next, we consider the welfare
effects of the two alternative reforms. The three bottom panels of Figure 10 plot
the welfare gains/losses of generations retiring between 2000 and 2110 in the case of
a delayed, FF reform and PAYGO, respectively.
Under this low-fertility scenario, the benchmark reform requires an even more
draconian adjustment. The replacement rate must be set equal to 35.6% as of
2012. Delaying the reform is now substantially more costly. A reform in 2040
requires a replacement rate of 29.8%, whereas a reform in 2100 requires a negative
replacement rate of -45.7%. The trade-off between current and future generations
becomes sharper than in the baseline economy. If we consider delaying the reform
until 2040, on the one hand, there are larger gains for the cohorts retiring between
2012 and 2039 relative to the benchmark reform (with gains ranging between 16%
and 17%). On the other hand, the delay is more costly for the future generations.
Aggregating gains and losses using a utilitarian welfare function yields a gain for
the high-discount planner of 6.4%, which is larger than in the benchmark economy.
This large gain is partly due to the fact that the population size is declining, so
the planner attaches a higher weight on more numerous earlier generations relative
to the baseline economy. The gain is as large as 10.5% if the reform is delayed
until 2100. However, the welfare loss for the future generations is also large, equal
to about 39%. The results are similar, albeit less extreme, for the low-discount
planner. For instance, delaying a reform until 2040 (2100) yields a welfare gain for
the low-discount planner of 2.6% (6.5%). In all cases, the gains are larger than in the
baseline model. The FF reform exhibits larger losses than in the baseline model (even
the low-discount planner prefers the benchmark to a fully funded reform). Moreover,
the PAYGO reform yields larger gains than in the benchmark reform (16.5% with
the high-discount and 5.3% with the low-discount planner, respectively). Part of the
reason is that with low population growth, the planner attaches a higher relative
weight to the early generations, who are the winners in this scheme.
In summary, lower fertility increases the magnitude of the adjustment required
to restore the intertemporal balance of the pension system. It also widens the gap
between the losses and gains of different generations in the alternative reforms.
C.
High interest rate
In the macroeconomic literature on pension reforms in developed economies, it
is common to assume that the return on the assets owned by the pension fund is
equal to the marginal return to capital (cf. Auerbach and Kotlikoffhor, 1987). In
this paper, we have calibrated the return on assets to 2.5%. However, the empirical
rate of return on capital in China has been argued to be much higher (see discussion
above). To get a sense of the role of this assumption, we now consider a scenario
in which the interest rate is much higher – equal to 6% – between 2012 and 2050.
We assume that the period of high interest rate will eventually come to an end as
China becomes fully industrialized. According to the macroeconomic model laid out
26
in section VI below, the year 2050 is roughly the end of this transition.
There are two main differences between the scenarios with lower and higher interest
rates. First, delaying the reform yields much smaller gains for the transitional
generations, and in fact the low-discount planner is essentially indifferent between
the benchmark reform and a delay until 2040, which she strictly prefers over delaying
until 2100. Second, the FF reform entails larger gains for the future generations and
smaller losses for the current generations relative to the baseline calibration. As
should be expected, when the interest rate is significantly higher than the average
growth rate, the PAYGO system becomes less appealing, because the gains to current
generations are smaller. In particular, the low-discount planner prefers the FF to
the PAYGO reform, although both are dominated by the benchmark reform.
VI.
A dynamic general equilibrium model
Up to now, we have taken the wages and the rate of return on savings as exogenous.
As we demonstrated in section V, the normative predictions hinge on the assumed
wage growth. In this section, we construct a dynamic general equilibrium model that
delivers the wage and interest rate sequence assumed in the baseline model of section
III as an equilibrium outcome. These prices are sufficient to compute the optimal
decisions of workers and retirees (consumption and labor supply) as well as the
sequence of budget constraints faced by the government. Therefore, the allocations
and welfare analyses of the previous section carry over to the general equilibrium
environment. The model is closely related to Song, Storesletten and Zilibotti (2011),
augmented with the demographic model of section II and the pension system of
section III.
A.
The production sector
The urban production sector consists of two types of firms: (i) financially integrated (F) firms, modeled as standard neoclassical firms; and (ii) entrepreneurial
(E) firms, owned by (old) entrepreneurs, who are residual claimants on the profits.
Entrepreneurs delegate the management of their firms to specialized agents called
managers. E firms can run more productive technologies than F firms (see Song,
Storesletten and Zilibotti, 2011, for the microfoundations of this assumption). However, they are subject to credit constraints that limit their size and their growth. In
contrast, the less productive F firms are unconstrained. Motivated by the empirical
evidence (see Song, Storesletten and Zilibotti, 2011) that private firms are more
productive and more heavily financially constrained than state-owned enterprises
(SOE) in China, we think of F firms as SOE and E firms as privately owned firms.
The technology of F and E firms are described, respectively, by the following
production functions:
YF = KFα (ANF )1−α ,
YE = KEα (χANE )1−α ,
where Y is output and K and N denote capital and labor, respectively. The parameter χ > 1 captures the assumption that E firms are more productive. A labor
market-clearing condition requires that NE,t +NF,t = Nt , where Nt denotes the total
urban labor supply at t, whose dynamics are consistent with the demographic model.
The technology parameter A grows at the exogenous rate zt ; At+1 = (1 + zt ) At .
The capital stock of F firms, KF,t , is not a state variable, since F firms have
access to frictionless credit markets, and capital is putty-putty (i.e., investment are
27
not irreversible). Thus, F firms can adjust the desired level of capital in every
period, irrespective of their past productive capacity. Let rtl denote the net interest
rate at which F firms can raise external funds. Let w denote the market wage. Profit
− 1
1−α
, where δ is the depreciation
maximization implies that KF = ANF α/ rtl + δ
rate. The capital-labor ratio and the equilibrium are determined by rl . Thus,
(6)
wt ≥ (1 − α)
α
l
rt + δ
α
1−α
At .
As long as there are active F firms in equilibrium (NF > 0), equation (6) holds with
strict equality.
Let KE,t denote the capital stock of E firms. E firms are subject to an agency
problem in the delegation of control to managers. The optimal contract between
managers and entrepreneurs requires revenue sharing. We denote by ψ the share of
the revenue accruing to managers.23 Profit maximization yields, then, the following
optimal labor hiring decision:
1−α
α
NEt = arg max (1 − ψ) (KEt ) χAt Ñt
(7)
− wt Ñt
Ñt
= ((1 − ψ) χ)
1
α
rtl + δ
α
1
1−α
KEt
.
χAt
The gross rate of return to capital in E firms is given by
α
(8)
ρE,t = (1 − ψ) KEt
(χAt NEt )1−α − wt NEt + (1 − δ) KEt /KE,t .
We assume that E firms are also subject to a credit constraint, modeled as in Song,
Storesletten and Zilibotti (2011, p. 216). According to such a model, E firms can
borrow funds at the same interest rate as F firms, but the incentive-compatibility
constraint of entrepreneurs implies that the share of investments financed externally
must satisfy the following constraint:
(9)
KE − ΩE,t ≤
ηρE
KE ,
1 + rl
where ΩE,t denotes the stock of entrepreneurial wealth invested in E firms at t, and,
hence, KE − ΩE,t denotes the external capital of E firms.
Three regimes are possible: (i) during the first stage of the transition, the credit
constraint (9) is binding and F firms are active (hence, the wage is pinned down
by (6) holding with equality); (ii) during the mature stage of the transition, the
credit constraint (9) is binding and F firms are inactive; (iii) eventually, the credit
constraint (9) ceases to bind (F firms remain inactive). In regimes (ii) and (iii), (6)
holds with strict inequality.
Consider, first, regime (i). Substituting NEt and wt into (8) by their equilib23 Managers have special skills that are in scarce supply. If a manager were paid less than a share ψ of
production, she could ”steal” it. No punishment is credible, since the deviating manager could leave the
firm and be hired by another entrepreneur. See Song, Storesletten and Zilibotti (2011) for a more detailed
discussion.
28
rium expressions, (6) and (7), yields the gross rate of return to E firms: ρE,t =
1−α (1 − ψ) ((1 − ψ) χ) α rtl + δ + (1 − δ) . The corresponding gross rate of return to
entrepreneurial investment is given by RE,t = ρE,t KE,t − 1 + rtl (KE,t − ΩE,t ) /ΩE,t .
1
1−α
We assume that (1 − ψ) α χ α > 1, ensuring that the return to capital is higher in
E firms than in F firms (i.e., that RE,t > rtl + 1). Note that the rate of return to
capital is a linear function of rtl in both E and F firms. The equilibrium in regime (i)
is closed by the condition that employment in the F sector is determined residually,
namely,
1
l
1
rt + δ 1−α KEt
NF,t = Nt − ((1 − ψ) χ) α
≥ 0.
α
χAt
Consider, next, regime (ii), where only E firms are active (NE,t = Nt ) and the
borrowing constraint is binding, so (9) holds with equality. In this case, the rates
of return to capital and labor equal their respective marginal products. More formally, wt = (1 − α) (1 − ψ) (χAt )1−α (KE,t /Nt )α , and the gross rate of return on
entrepreneurial wealth is given by
KEt α−1
1−α
ρE,t = α (1 − ψ) χ
+ (1 − δ) ,
At N t
ηρE,t
ΩE,t . Given
whereas the borrowing constraint implies that KE,t = 1 + Rl −ηρ
E,t
the stock of entrepreneurial wealth, ΩE,t , the two last equations pin down ρE,t and
KE,t . The rate of return to entrepreneurial investment is then determined by the
expression used for regime (i).
Finally, in regime (iii) the rate of return to capital in E firms is identical to the
rate of return offered by alternative investment opportunities (e.g., bonds). Namely,
RE,t = 1 + rtl .
Thus, KE,t ceases to be a state variable, and the wage is given by
α/(1−α)
wt = (1 − α) α/ rtl + δ
χAt .
In all regimes, the law of motion of entrepreneurial wealth is determined by the
optimal saving decisions of managers and entrepreneurs, described below.
The rural production sector consists of rural firms whose technology is assumed
αR
to be similar to that of urban F firms, YRt = KRt
(χR At NRt )1−αR , where χR < 1.
Like urban F firms, rural firms can raise external funds at the interest rate rtl in each
period, and adjust their capital accordingly. So, rtl pins down capital-labor ratio and
wage in the rural economy. This description is aimed to capture, in a simple way,
the notion that there are constant returns to labor in rural areas, due to, e.g., rural
overpopulation.
B.
Banks
Competitive financial intermediaries (banks) with access to perfect international
financial markets collect savings from workers and hold assets in the form of loans
to domestic firms and foreign bonds. Foreign bonds yield an exogenous net rate of
return denoted by r, constant over time. Arbitrage implies that the rate of return
29
on domestic loans, rtl , equals the rate of return on foreign bonds, which in turn must
equal the deposit rate. However, lending to domestic firms is subject to an iceberg
cost, ξ, which captures the operational costs, red tape, and so on, associated with
granting loans. Thus, ξ is an inverse measure of the efficiency of intermediation.
In equilibrium, rd = r and rtl = (r + ξt ) / (1 − ξt ) , where rtl is the lending rate to
domestic firms.
C.
The households’ saving decisions
Workers and retirees face the problem discussed in section III, given the equilibrium wage sequence, and having defined R ≡ 1 + r. As in the previous section, we
hold fixed the share of workers participating in the pension system.
The young managers of E firms earn a managerial compensation m. Throughout their experience as managers, they acquire skills enabling them to become entrepreneurs at a later stage of their lives. The total managerial compensation in
period t equals Mt = ψYE,t . Managers work for JE years, and during this time
can only invest their savings in bank deposits (as can workers). As they reach age
JE + 1, they must quit (i.e., retire as managers) and can become entrepreneurs. In
this case, they invest their wealth in their own business yielding the annual return
RE,t and hire managers and workers. Thereafter, they are the residual claimants
of the firm’s profits. We assume that entrepreneurs are not in the pension system.
Their lifetime budget constraint is then given by
J
JE
J
sj
ct+j +
Rj
j=0
E
sj
sj
1
ct+j =
m .
j t+j
RJE Πt+j
R
v=t+JE +1 RE,ν
j=0
j=JE +1
D.
Mechanics of the model
The dynamic model is defined up to a set of initial conditions including the wealth
distribution of entrepreneurs and managers, the wealth of the pension system, the
aggregate productivity (A0 ), and the population distribution. The engine of growth
is the savings of managers and entrepreneurs. If the economy starts in regime (i),
then all managerial savings are invested in the entrepreneurial business as soon
as each manager becomes an entrepreneur. As long as managerial investments are
sufficiently large, the employment share of E firms grows and that of F firms declines
over time.
The comparative dynamics of the main parameters is as follows: (i) a high β
implies a high propensity to save for managers and entrepreneurs and a high speed
of transition; (ii) a high world interest rate (r) and/or a high iceberg intermediation
cost (ξ) increases the lending rate, implying a low wage, a high rate of return in
E firms, a high managerial compensation, and, hence, a high speed of transition;
(iii) a high productivity differential (χ) implies a high rate of return in E firms, a
high managerial compensation, and, hence, a high speed of transition; (iv) a high
σ implies that entrepreneurs can leverage up their wealth and earn a higher return
on their savings, which speeds up the transition; and (v) a high managerial rent (ψ)
implies a low rate of return in E firms, a high managerial compensation, and, hence,
has ambiguous (and generally non-monotonic) effects on the speed of transition.
Note that the savings of the worker do not matter for the speed of transition,
because the lending rate offered by banks depends only on the world market interest
rate and on the iceberg cost.
30
E.
Calibration
We must calibrate two parameters related to the financial system, ξ and σ, and four
technology parameters, α, δ, χ and ψ. The parameters α and δ are set exogenously:
α = 0.5 so that the capital share of output is 0.5 in year 2000 (Bai, Hsieh and Qian,
2006), and δ = 0.1 so that the annual depreciation rate of capital is 10%.
The remaining parameters are calibrated internally, so as to match a set of empirical moments. We set the parameters ψ and χ so that the model is consistent
with two key observations: (i) the capital-output ratio in E firms is 50% of the
corresponding ratio in F firms (as documented by Song, Storesletten and Zilibotti
(2011) for manufacturing industries, after controlling for three-digit industry type),
(ii) the rate of return on capital is 9% larger in E firms than in F firms.24 The
implied parameter values are ψ = 0.27 and χ = 2.73. This implies that the TFP of
an E firm is 1.65 times of the TFP of an F firm.25
We set ξ so as to target an average gross return on capital of 20% in year 2000
(Bai, Hsieh and Qian, 2006). With δ = 10%, this implies an average net rate
of return on capital of 10%. This average comprises both F firms and E firms.
Since the DPE employment share in the period 1998-2000 was on average 10%, this
implies ρF = 9.3%, so that the initial value for ξ is ξ2000 = 0.062. After year 2000,
we assume that there is gradual financial improvement so ξ falls linearly to zero
by year 2024. The motivation for such decline is twofold. First, we believe it is
reasonable that banks improve their lending practices over time, so that borrowinglending spreads will eventually be in line with corresponding spreads in developed
economies. Second, a falling ξ will generate capital deepening in F firms and E
firms due to cheaper borrowing and higher wages, respectively. Such development
helps the model to generate an increasing aggregate investment rate during 20002009, which is a clear pattern of aggregate data. If ξ were constant, the model
would predict a falling rate (see Song, Storesletten and Zilibotti, 2011, for further
discussion).
We set σ = 0.43, so that entrepreneurs can borrow 87 cents for each dollar in
equity in 2000. This value for σ implies that the growth in the DPE employment
share is in line with private employment growth between 2000 and 2008 in urban
areas. We set the initial level of productivity, A2000 , so that the urban GDP per
capita is 20% of the US level in 2011. Moreover, we set the growth rate of At (i.e.,
the secular exogenous productivity growth) so that the model generates an aggregate
growth in GDP per capita of 9.7% for China during 2000-2011. The resulting growth
rate in At is 2% larger than the associated world growth rate during this period.
After 2011, this excess growth in At falls linearly to zero until the TFP level in E
firms is equal to that of US firms. This occurs in year 2022. Finally, β is calibrated
to 1.0175 to match the average aggregate saving rate of 48.2% in 2000-2010.
In the rural sector, we set αR = 0.3 to match the observed 20% investment rate in
the rural area in 2000. The technology gap χR is set to 0.75 to capture an observed
urban-rural wage gap of 1.84 in 2000. The rural wage grows over time, due to the
exogenous technology growth and to the decreasing lending rate. The rural-urban
24 Song, Storesletten and Zilibotti (2011) document that manufacturing, domestic private enterprises
(DPE) have on average a ratio of profits per unit of book-value capital 9% larger than that of SOEs
during the period 1998-2007. A similar difference in rate of return on capital is reported by Islam, Dai and
Sakamoto (2006).
25 Hsieh and Klenow (2009) estimate TFP across manufacturing firms in China and find that the TFP of
DPEs is about 1.65 times larger than the TFP of SOEs.
31
wage gap implied by the model increases from 1.84 in 2000 to 3.47 in 2040 and stays
constant thereafter (see Figure C-3 in Appendix C).
The initial conditions are set as follows. Total entrepreneurial wealth in 2000
is set equivalent to 14.6% of urban GDP so that the 2000 DPE employment is
20%. The distribution of that entrepreneurial wealth is obtained by assuming that
all entrepreneurs are endowed with the same initial wealth in 1992 (1992 is the
year when free-market reforms in China accelerated). Moreover, all managers are
assumed to start with zero wealth in 1992. Initial wealth for workers and retirees is
also set to zero in 1992. The 2000 distribution of wealth across individuals is then
derived endogenously. Finally, the initial government wealth is set to 71% of GDP
in 2000 so as to generate a net foreign surplus equal to 12% of GDP in 2000.
F.
Simulated output trajectories
The calibrated model yields growth forecasts that we view as plausible. Figure 11
shows the evolution of productivity and output per capita forecasted by our model.
The growth rate of GDP per worker remains about 8.5% per year until 2020 (see
upper panel). After 2020, productivity growth is forecasted to slow down. This is
driven by two forces: (i) the end of the transition from state-owned to private firms
and (ii) the slowdown in technological convergence. The growth rate remains above
6.9% between 2020-2030 and eventually dies off in the following decade. Note that
the growth of GDP per capita is lower than that of GDP per worker after 2015, due
to the increase in the dependency ratio. On average, China is expected to grow at
a rate of 6.5% between 2012 and 2040. The contribution of human capital is 0.8%
per year, due to the entry of more educated young cohorts in the labor force. In this
scenario, the GDP per worker in China will be 73% of the that in the US by 2039,
remaining broadly stable thereafter. Total GDP in China is set to surpass that in
the United States in 2013 and to become more than twice as large in the long run.
The wage sequence that was assumed in section III is now an endogenous outcome.
Wages are forecasted to grow at an average of 5.1% until 2030 and to slow down
thereafter. What keeps wage growth high after 2020 is mostly capital deepening.
G.
Sensitivity analysis
High savings and foreign surplus
Although the growth forecasts are plausible, the calibrated economy generates a
very large amount of savings. For instance, in 2070 the economy has a wealth-GDP
ratio equal to 1169%. This is because the model is calibrated to match aggregate
savings during 2000-2010. In that period, China experienced high growth and yet a
very high saving rate (48.2% on average).
Since our stylized model forecasts an eventual decline in growth, the intertemporal motive would suggest that consumption should have been high before 2010.
Therefore, the model requires a sufficiently high discount factor (β = 1.0175) in
order to predict the empirical saving rate during the first decade of the 21st century.
According to our model, the future saving rate will be even higher than today once
the wage growth declines – provided that the discount factor remains constant. In
our model, a high β is a stand-in for a number of institutional features that are
not explicitly considered and that may explain a high propensity to save over and
32
GDPpc and GDPpw growth
Annual Growth Rate
0.09
GDPpw
0.08
0.07
GDPpc
0.06
0.05
0.04
0.03
0.02
2010
2020
2030
2040
2050
Time
2060
2070
2080
2090
2100
2070
2080
2090
2100
GDP per Capita (Log Scale)
GDPpc: China and US
120000
60000
US
30000
China
15000
7500
2000
2010
2020
2030
2040
2050
Time
2060
Figure 11: The upper panel shows projected annual growth rates in GDP per worker and GDP per capita
in the calibrated economy. The lower panel shows projected GDP per capita in levels for China and the US.
beyond pure preferences (e.g., large precautionary motives or large downpayment
requirements for house purchases).26
Note that long-term wages and GDP do not hinge on the domestic propensity to
save (although the entrepreneurs’ propensity to save determines the speed of the
transition). The entrepreneurial firms grow out of their financial constraint by year
2039. Thereafter, domestic capital accumulation and wages are determined by the
world interest rate. In the long run, β only determines the foreign position, which
is predicted to reach 13.7 times GDP by 2070.
It seems implausible that China will accumulate such a large foreign surplus. One
might also be concerned that the high discount factor could affect our quantitative
welfare results. To address such concerns, we consider an alternative scenario, where
all cohorts entering the labor market after 2012 have β = 0.97. In such an alternative
scenario China’s net foreign position would be zero in the long run. The analysis
of the alternative pension arrangements yields essentially the same results as in the
high β economy. Thus, the calibration of β is unimportant for the effects of the
welfare analysis, which is the main contribution of this paper.
Financial development
The model borrows from Song, Storesletten and Zilibotti (2011) the assumption
that E firms are financially constrained. Note that the salience of the financial
constraints declines over time as E firms accumulate capital. As the economy enters
regime (iii), which occurs in 2038, the financial constraint ceases to bind.
26 Chamon, Liu and Prasad (2010) and Song and Yang (2010) study household savings in calibrated lifecycle models. They incorporate individual risk and detailed institutional features of the pension system
and find that their models are qualitatively consistent with the life-cycle profile of household saving rates.
However, both studies find that with a conventional choice of β, their models would imply quantitatively
too low savings for the young households.
33
In our baseline calibration, the parameter σ, which regulates borrowing of private
firms, is assumed to be constant over time. An exogenous increase in σ – for example,
due to financial development – would speed up growth of private firms. Wage growth
would accelerate earlier, although the long-run wage level would be unaffected.
To study the effects of financial development on pension reform, we consider a
stark experiment in which the borrowing constraint on private firms is completely
removed in 2012. This means that state-owned firms vanish, and there is large
capital inflow driven by entrepreneurial borrowing. Wages jump upon impact (by
85%) due to the large capital deepening. In 2030, the wage level is still 15.8% above
the baseline calibration. In 2038 the wage level is the same as in the benchmark
calibration.
Although financial development affects the transition path, it brings little change
to the conclusions of the welfare analysis. The benchmark reform requires a slightly
smaller reduction of the replacement rate: 40.7% instead of 40%. The delayed reform
still entails gains for the transition cohorts, albeit these gains decline faster over time.
For instance, delaying a reform until 2040 yields a 17% consumption equivalent gain
for the cohort retiring in 2012, but only a 12% gain for the cohort retiring in 2039.
The losses suffered by the cohorts retiring after 2040 are comparable in size to those
in the baseline scenario without financial development. The gains accruing to the
high- and low-discount planners are, respectively, 4.1% and 0.5% (5% and 0.8% in
the baseline scenario).
The FF reform yields slightly better outcomes. All generations retiring after
2050 gain from the reform (2058 in the baseline scenario), and the losses of the
earlier cohorts only reach 8% (11% in the baseline scenario). The high-discount
planner continues to prefer the benchmark reform to the FF reform, whereas the
low-discount planner continues to have the opposite ranking. The PAYGO reform
yields even larger gains to the earlier cohorts. Both the high- and the low-discount
social planners continue to prefer the PAYGO reform to any alternative reform
considered. However, the welfare gap between the PAYGO and the fully funded
reform is now smaller, since the planners dislike the concentrated nature of the
gains under the PAYGO reform. For instance, the consumption equivalent gain of
the low-discount planner relative to the benchmark reform is 1.1%, compared with
1.8% in the baseline scenario. Since the fully funded reform also entails a 0.6% gain
relative to the benchmark reform, the consumption equivalent gain of the PAYGO
relative to the FF reform is only 0.5% (although it remains significantly higher,
11.6%, for the high-discount planner).
In conclusion, financial development mitigates but does not change the welfare
implications of alternative reforms.
VII.
Conclusions
We have studied the welfare effects of alternative pension reforms with the aid
of a dynamic general equilibrium model. Our model – based on Song, Storesletten
and Zilibotti (2011) – is quantitatively consistent with the aggregate trends of the
Chinese economy in the first decade of the 21st century. In addition, it delivers
broadly plausible forecasts: wage growth will remain high (and possibly increase)
until about 2030; growth will eventually slow down, and China will become a mature
economy by about 2040.
A number of studies, based on aggregate demographic models, have argued that
China must reform its pension system to achieve long-run balance in response to a
34
sharp increase in the dependency ratio (see, e.g., Sin (2005), Dunaway and Arora
(2007), Salditt, Whiteford and Adema (2007), and Lu (2011)). Our analysis concurs
with this view, but shows that rushing into a draconian reform would have large
adverse effects on inequality: it would significantly harm current generations and
only mildly benefit future generations. In a fast-growing society like China, this
would imply dispensing with a powerful institution redistributing resources from
richer future generations to poorer current generations. Under standard welfare
criteria, a straight pay-as-you-go system would be preferred to both the draconian
reform and to a reform that pre-funds the pension system.
Our model delivers very different predictions in a mature economy with low wage
growth and perfect capital markets. In this case, a fully funded system outperforms a
pay-as-you-go system. These contrasting results highlight the general principle (see
e.g. Acemoglu, Aghion and Zilibotti, 2006) that mechanically transposing policy
advice from mature to developing or emerging economies may be misleading.
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1
APPENDIX
A.
Estimation method of the rural-urban migration
In this appendix, we present the estimation method of the rural-urban migration.
and nh,i,j
2005 represent the population of group (h, i, j) in the 2000 census and
2005 survey, respectively, where h ∈ {u, r}, i ∈ {f, m}, and j ∈ {0, 1, · · · , 100}
stand for residential status (u for urban and r for rural residents), gender (f for
females and m for males), and age, respectively. n̂h,i,j
2005 represents the projected
“natural”population in 2005. Denote mi,j the net flow of the rural-urban migration
from 2000 to 2005. The 2005 urban and rural population gender-age structure can
thus be composed into three parts:
nh,i,j
2000
(A-1)
u,i,j
i,j
nu,i,j
+ εu,i,j ,
2005 = n̂2005 + m
(A-2)
r,i,j
i,j
nr,i,j
+ εr,i,j ,
2005 = n̂2005 − m
where εh,i,j captures measurement errors in the census and survey.
In the ideal case with no measurement errors, either (A-1)
can back
or (A-2)
h,i,j , is small.
out mi,j . The measurement error on the total population,
ε
h,i,j
When h,i,j εh,i,j = 0, (A-1) and (A-2) imply that the projected total population,
h,i,j
h,i,j
h,i,j n̂2005 , would be equal to the total population in the 2005 survey,
h,i,j n2005 .
h,i,j
27 However,
The difference between h,i,j n̂h,i,j
2005 and
h,i,j n2005 is less than 1%.
the match of the sum of the rural and urban population in each gender-age group
is less perfect. Figure A-1 plots the projected 2005 “natural”population genderage structure (solid line) and the 2005 survey data (dotted line). The discrepancy
between the two lines reveals the measurement error on the population of each
gender-age group, εi,j , where
h,i,j
(A-3)
εi,j ≡
εh,i,j =
n2005 − n̂h,i,j
2005 .
h
h
Figure A-1 suggests εi,j to be quantitatively important.28 To understand how εi,j
affects the estimated migration gender-age structure, let us assume the measurement
error on urban population, εu,i,j , is proportional to εi,j :
(A-4)
εu,i,j = φ · εi,j ,
where φ ∈ [0, 1]. It follows that the measurement error on rural population is
(A-5)
εr,i,j = (1 − φ) · εi,j .
27 Despite the small discrepancy, to avoid biased estimates, we adjust nh,i,j by a scale of κ, where κ is
2000
calibrated to 1.0073 by matching the projected 2005 total population with the 2005 survey data. κ = 1.0073
suggests the discrepancy of the total population to be less than 1%.
28 If all the discrepancies are due to sampling errors in the 2005 survey, the comparison between the two
lines in Figure A-1 indicates that a major drawback of the 2005 survey is the undercounted young labor
force (age 16 to 40). Our calculation suggests 66 million young labor force (11% of total young labor force)
missing from the 2005 survey.
2
15
Panel A: Female Population
6
x 10
Simulation
Data
10
5
0
15
0
10
20
30
40
50
Age
60
70
80
90
100
Panel B: Male Population
6
x 10
Simulation
Data
10
5
0
0
10
20
30
40
50
Age
60
70
80
90
100
Figure A-1: The upper panel shows the female population of different ages in 2005, in the survey data (red
solid line), and in our simulation (blue dashed line). The lower panel shows the male population in 2005.
Rearranging (A-1) gives the net flow of migration:
u,i,j
(A-6)
mi,j =
εi,j
n2005 − n̂u,i,j
2005 − φ
i
i
j
=
j
i
nu,i,j
2005
j
−
n̂u,i,j
2005
i
−φ
j
h
i
nh,i,j
2005
j
−
n̂h,i,j
2005
.
The second equality comes from (A-3). Let us consider two extreme cases of φ.
When φ = 1, (A-6) can be written as
r,i,j
r,i,j
n̂2005
mi,j =
n2005
−
.
i
j
i
j
projected “natural”rural population
When φ = 0, (A-6) reduces to
u,i,j
mi,j =
n2005
i
j
i
j
urban population in the survey data
i
j
n̂u,i,j
2005
rural population in the survey data
−
i
j
.
projected “natural”urban population
Therefore, the choice of φ boils down to the choice of using rural or urban population
to back out migration. It has been widely acknowledged that urban population
survey tends to underestimate “floating population,”that is, rural migrants without
hukou - the local household registration status (e.g. Liang and Ma, 2004). So, we
set φ = 1. We will discuss the results using φ = 0.5.
3
It is instructive to compare the actual migration structure with our estimates. The
migration flow structure is hard to obtain. However, the migration stock structure
may shed some light on the flow structure. The age structure of migrants in the 2000
census is presented in the second row of Table A-1, which has a high concentration
in the 15-29 age group. The same pattern also appears in our estimates under φ = 1
(the third row). φ = 0.5 results in a much more dispersed age structure (the fourth
row). This provides a justification for using φ = 1.29
Table A-1:
Age distribution of migration (percent)
age
migration stock in the 2000 census
estimated flow from 2000 to 2005 with φ = 1
estimated flow from 2000 to 2005 with φ = 0.5
<15
9.0
25.8
17.8
15-29
60.5
64.8
39.5
30-44
22.2
26.5
27.7
45-59
5.8
-8.6
8.9
60+
2.5
-8.6
6.1
Note: The age structure in the 2000 census is from (Liang and Ma, 2004).
Finally, we compute mri,j , the age–gender specific migration rate defined as the
average annual net flow of migration per hundred rural population with gender i and
age j. We assume that mri,j is time-invariant and the mortality rates for migrants
are the same as those for rural residents. Then, mi,j can be written as follows:
r,i,j−1
r,i,j−5
mi,j = mri,j−5 nr,i,j−5
1
−
d
·
·
·
1
−
d
2000
2000
2000 migration of 2000
survival rate from 2000 to 2005
r,i,j−1
r,i,j−5
+ mri,j−4 1 − mrr,j−5 nr,i,j−5
1
−
d
·
·
·
1
−
d
2000
2000
2000
migration of 2001
survival rate from 2001 to 2005
r,i,j−1
r,i,j−5
+ mri,j−3 1 − mrr,j−4 1 − mrr,j−5 nr,i,j−5
1
−
d
·
·
·
1
−
d
2000
2000
2000
migration of 2002
survival rate from 2001 to 2005
r,i,j−1
r,i,j−5
+ mri,j−2 1 − mrr,j−3 1 − mrr,j−4 1 − mrr,j−5 nr,i,j−5
1
−
d
·
·
·
1
−
d
2000
2000
2000
migration of 2003
survival rate from 2001 to 2005
r,i,j−1
r,i,j−5
+ mri,j−1 1 − mrr,j−2 · · · 1 − mrr,j−5 nr,i,j−5
.
1
−
d
·
·
·
1
−
d
2000
2000
2000
migration of 2004
survival rate from 2001 to 2005
Here, nr,i,j−5
is the mortality rate of rural residents in the 2000 census. In other
2000
words, mi,j measures an accumulated migration stock from 2000 to 2005. The above
equation allows us to back out the age-gender specific migration rates. Specifically,
for j = J + 5:
r,i,J+4
r,i,J+4
mi,J+5 = mri,J n̂r,i,J
1
−
d
·
·
·
1
−
d
2000
2000
2000 migration of 2000
survival rate from 2000 to 2005
29 One caveat is that the data from the 2000 census are the age structure of narrowly defined migrants,
whereas our estimate is on broadly defined migrants including urbanized population.
4
⇒
mri,J =
nr,i,J
2000
For j = J + 4:
mi,J+5
.
r,i,J+4
r,i,J
1 − d2000
· · · 1 − d2000
r,i,J+3
r,i,J−1
mi,J+4 = mri,J−1 n̂r,i,J−1
1
−
d
·
·
·
1
−
d
2000
2000
2000 migration of 2000
⇒
+ mr
mri,J−1
i,J
survival rate from 2000 to 2005
r,J−1
1 − mr
r,i,J+3
r,i,J−1
1
−
d
·
·
·
1
−
d
nr,i,J−1
2000
2000
2000
migration of 2001
survival rate from 2000 to 2005
r,i,J+3
r,i,J−1
mi,J+4 − mri,J nr,i,J−1
1
−
d
·
·
·
1
−
d
2000
2000
2000
.
=
r,i,J+3
r,i,J−1
(1 − mri,J ) nr,i,J−1
1
−
d
·
·
·
1
−
d
2000
2000
2000
All the migration rates can thus be solved in a recursive way.
B.
Details on the Chinese pension system
This appendix provides a description of the basic features of the Chinese pension
system. We start with the urban pension system, and then provide a brief description
of the rural pension system, which has been introduced experimentally in 2009.
B1.
The urban pension system
The pre-1997 urban pension system was primarily based on state and urban collective enterprises in a centrally planned economy. Retirees received pensions from
their employers, with replacement rates that could be as high as 80 percent (see
e.g. Sin, 2005; Salditt, Whiteford and Adema, 2007). The coverage was low in the
work-unit-based system, though. Many non-state-owned enterprises had no pension
scheme for their employees. The coverage rate, measured by the ratio of the number of workers covered by the system to the urban employment, was merely 44%
in 1992 according to China Statistical Yearbook 2009 (National Bureau of Statistics
of China, 2010). The rapid expansion of the private sector caused a growing disproportion between the numbers of contributors and beneficiaries and, therefore, a
severe financial distress for the old system (Zhao and Xu, 2002). To deal with the
issue, the government initiated a transition from the traditional system to a public
pension system in the early 1990s. The new system was implemented nationwide
after the State Council issued “A Decision on Establishing a Unified Basic Pension
System for Enterprise Workers (Document 26)”in 1997.
The reformed system mainly consists of two pillars. The first pillar, funded by 17%
wage taxes paid by enterprises, guarantees a replacement rate of 20% of local average
wage for retirees with a minimum of 15 years of contribution. It is worth emphasizing
that the pension fund is managed by local governments (previously at the city level
and now at the provincial level). The second pillar provides pensions from individual
accounts financed by a contribution of 3% and 8% wage taxes paid by enterprises and
workers, respectively. There is a third pillar adding to individual accounts through
voluntary contribution. The return of individual accounts is adjusted according to
bank deposit rates. The system also defines monthly pension benefits from individual
5
accounts equaling the account balance at retirement divided by 120. The targeted
replacement rate of the system is 58.5%.30
More recently, a new reform was implemented after the State Council issued “A
Decision on Improving the Basic Pension System for Enterprise Workers (Document
38)”in 2005. The reform adjusted the proportion of taxes paid by enterprises and
individuals and the proportion of contribution for individual accounts. Individual
accounts are now funded by the wage taxes of 8% paid by workers only.31
Two features of the current urban pension system is particularly important for
our modeling. First, the pension reform was cohort-specific. There were three types
of cohorts when the pension reform took place: Cohorts enter into the labor market
after 1997 (Xinren), cohorts retired before 1997 (Laoren) and cohorts in between
(Zhongren). Pension contributions and benefits of Xinren are entirely determined
by the new rule. According to Item 5 in Document 26, the government commits to
pay Laoren the same pension benefits as those in the old system subject to an annual
adjustment by wage growth and inflation. For Zhongren, their contributions follow
the new rule, while their benefits consist of two components: (1) pensions from the
new system identical to those for Xinren, and (2) a transitional pension that smooths
the pension gap between Laoren and Xinren. For simplicity, we ignore Zhongren and
take pensioners retiring before and after 1997 as Laoren and Xinren, respectively.
Following Sin (2005), we set the replacement rate for Laoren and Xinren to 78%
and 60%, respectively.
Second, like private savings, pension funds are allowed to invest in domestic stock
markets. The baseline model assumes the annual rate of returns to pension funds
to be 2.5%, which is identical to the rate of returns to private savings. According to
the latest information released by the National Council for Social Security Fund, the
average share of pension funds invested in stock markets was 19.22% in 2003-2011.32
If 20% of pension funds have access to the market with an annual return of 6% and
the rest of the funds gain an annual return of 1.75% as the one-year bank deposits,
the average annual rate of returns would be equal to 2.6%, almost equal to 2.5% set
in the baseline model.
It is also worth emphasizing that the actual urban pension system deviates from
statutory regulations in a number of ways and our model has been adapted to
capture some major discrepancies. First, the individual accounts are basically empty.
Despite the recent efforts made by the central government to fund these empty
individual accounts, there are only 270 billion RMB in all individual accounts of
around 200 million workers participating in the urban pension system.33 Therefore,
we take the individual accounts as notional and ignore any distinction between the
different pension pillars throughout the paper. In addition, we assume that 40% of
30 Suppose that the wage growth rate is equal to the interest rate. For a worker who contributes to the
system for 35 years (from age 25 to 60), her pension benefits should be equal to 20% of the local average
wages (the first pillar) plus 38.5% of her wage before retirement.
31 The reform also adjusted the pension benefits. The replacement rate of an individual is now determined
by years of contribution: A one year contribution increases the replacement rate of a wage index averaged
from local and individual wages by one percentage point. However, the article did not state explicitly how
to compute the wage index.
In practice, the index appears to differ across provinces. For instance, the increase in the average pension
benefits per retiree in 2011 was almost the same across Beijing and GanSu (the monthly increase was
RMB210 in Beijing and RMB196 in GanSu), though the average wage in Beijing is more than two times as
high as that in GanSu and the gap has been rather stable over time.
32 Source: http://www.ssf.gov.cn/xw/xw gl/201205/t20120509 4619.html.
33 The number of 270 billion RMB comes from the information released by the Ministry
of Human Resources and Social Security in the 2012 National People’s Congress.
Source:
http://lianghui.people.com.cn/2012npc/GB/239293/17320248.html
6
pension benefits are indexed to wage growth. The level of indexation is set on the
conservative side since the actual level is between 40% and 60% (see Sin, 2005).
Second, the statutory contribution rate including both basic pensions and individual accounts is 28%, of which 20% should be paid by firms and 8% should be paid
by workers (see the above discussion on Document 26 and 38). However, there is
evidence that a significant share of the contributions is evaded. For instance, in the
annual National Industrial Survey – which includes all state-owned manufacturing
enterprises and all private manufacturing enterprises with revenue above 5 million
RMB – the average pension contributions paid by firms in 2004-2007 amounts to
11% of the average wages, 9 percentage points below the statutory rate.34 Most
evasion comes from privately owned firms, whose contribution rate is a merely 7%.
The actual contribution rate is substantially lower than the statutory rate even
for workers participating in the system. A simple way of estimating the actual
contribution rate conditional on participation is to look at the following ratio:
BR ≡
≡
per retiree pension benefits
per worker pension contributions
total pension fund expenditure
total retirees covered by the system
total pension fund revenue - government subsidy
total workers covered by the system
.
If the replacement rate is indeed 60%, a contribution rate of 28% would imply BR
to be 2.1. However, we find that the average BR in the data from 1997 to 2009
is 3.1, much higher than 2.1 by the statutory contribution rate. With a targeted
replacement rate of 60%, the ratio of 3.1 would imply an actual contribution rate of
19.4%.35 So, we set the actual contribute rate to 20% in the paper.
Finally, although the coverage rate of the urban pension system is still relatively
low, it has grown from about 40% in 1998 to 57% in 2009, where we measure the
coverage rate by the number of employees participating in the pension system as
a share of the number of urban employees.36 There is a concern that the rapidly
growing size of migrant workers might lead to downward-biased urban employment.
Our estimation suggests that the urban population (including migrants) between
age 22 and 60 increases by 130 million from 2000 to 2009. A labor participation rate
of 80% would imply an increase of 104 million in the urban employment, whereas
the increase by the official statistics is 79 million. Restoring the 25 million “missing”urban employment would lower the pension coverage rate from 57% to 53%
in 2009. Our baseline model assumes a constant coverage rate of 60%, reflecting a
trade-off between the low coverage of the current pension system and the potentially
higher one in the future.
34 In
addition, with a labor income share less than 20%, wages appear to be severely underreported.
the data are available from China Statistical Yearbook (National Bureau of Statistics of China,
2010), except for the government subsidies. Fortunately, since 2010, the Ministry of Finance has started to
publicize detailed expenditure items. The government subsidy to the pension fund amounted to 191 billion
RMB in 2010, accounting for 21% of the total government social security and employment expenditure. We
then use 21% to back out annual government subsidy to pension funds from annual total government social
security and employment expenditure, which is available from China Statistical Yearbook.
36 Both numbers are obtained from China Statistical Yearbook 2010.
35 All
7
B2.
The rural pension system
The pre-2009 rural pension program had two features. First, it was “fully-funded”in
the sense that pension benefits were essentially determined by contributions to individual accounts. Second, the coverage rate was low since farmers did not have
incentives to participate. A pilot pension program was launched for rural residents
in 2009. Like those in the urban pension system, the new rural program entails two
benefit components. The first one is referred to as basic pension, mainly financed
by the Ministry of Finance, and the second one is pension from individual account.
If a migrant worker who joined the urban pension system returns to her home town,
the money accumulated in her account will be transferred to her new account in
the rural pension program. The program was first implemented in 10% of cities and
counties on a trial basis. The government targeted to extend the program to 60% of
cities and counties in 2011. Many of the cities and counties report high participation
rates (above 80%). This is not surprising since the program is heavily subsidized
(see below for more details).
We then lay out some basic features of the new program upon which the model is
based. According to “Instructions on New Rural Pension Experiments”issued by the
State Council in 2009, the new program pays a basic pension of RMB55 ($8.7) per
month. Suppose that the rural wage equals the rural per capita annual net income,
which was RMB5153 in 2009 (National Bureau of Statistics of China, 2010). Then,
the basic pension would correspond to a replacement rate of 12.8%. Notice that
provinces are allowed to choose more generous rural pensions. So, the replacement
rate of 9% should be viewed as a lower bound.37 In practice, some places set a much
higher basic pension standard. Beijing, for instance, increased the level to RMB280.
The monthly basic pension in Shanghai has a range from RMB150 to RMB300,
dependent of age, years of contribution and status in the old pension program.38
Since the rural per capita net income in Beijing and Shanghai is about 1.4 times
higher than the average level in China, a monthly pension of RMB280 would imply a
replacement rate of 27.2%. In the quantitative exercise, we then set the replacement
rate to 20% to match the average of the basic level of 12.8% and the high level of
27.2%.39 On the contribution side, rural residents in principle should contribute 4%
to 8% of the local average income per capita in the previous year. We take the mean
and set a contribution rate of 6%.40
The current pension program heavily relies on government subsidy. China Statistical Yearbook 2010 reports a rural population of 712.88 million. According to
the 2005 one-percent population survey, 13.7% of rural population is above age 60.
37 The Ministry of Human Resources and Social Security has made it clear that there is no upper bound for
basic pension and local governments may increase basic pension according to their public financing capacity.
38 See “Detailed Rules for the Implementation of Beijing Urban-Rural Household Pension Plans,”Beijing
Municipal Labor and Social Security Bureau, 2009 and “Implementation Guidelines of State Council’s Instructions on New Rural Pension Experiments,”Shanghai Municipal Government, 2010.
39 All rural residents above age 60 are entitled to basic pension. The only condition is that children of
a basic pension recipient, if any, should participate in the program. In practice, basic pension might be
contingent on years of contribution and status in the old pension program (see the above example from
Shanghai).
In addition, a recent official policy report from the Ministry of Human Resources and Social Security
(http://news.qq.com/a/20090806/000974.htm) states that by the rule of the new system, a rural worker
paying an annual contribution rate of 4% for 15 years should be entitled to pension benefits with a replacement rate of 25%.
40 Rural residents are allowed to contribute more. But the contribution rate cannot exceed 15% for each
person. Moreover, to be eligible for pension from individual account, a rural resident must contribute to
the program for at least 15 years. The monthly pension benefit is set equal to the accumulated money in
individual account divided by 139 (the same rule applied to the urban pension program).
8
These two numbers give a rural population of 97.66 million who are entitled to basic
pension. This, in turn, implies an annual government subsidy of 64.46 billion RMB,
if monthly basic pension is set to RMB55. The central government revenue is 3592
billion RMB in 2009. So, a full-coverage rural pension program in 2009 would require subsidy as a share of the central government revenue of 1.8% and a share of
GDP of 0.19%.
C.
Additional figures
Years of Schooling by Cohort
12
11
10
Years of Schooling
9
8
7
6
5
4
3
2
1930
1940
1950
1960
1970
Birth Year
1980
1990
2000
2010
Figure C-1: The figure shows the average number of years of schooling for different age cohorts in China.
Source: Barro and Lee data set. The values after 1990 are (linearly) extrapolated, assuming the growth in
schooling accumulation stagnates at 12 years.
9
Panel a: Replacement Rate by Year of Retirement
0.8
0.6
0.4
0.2
1960
1980
2000
2020
2040
2060
2080
2100
Time
Panel b: Tax Revenue and Pension Expenditures as Shares of Urban Earnings
0.2
Expenditures, Delayed Reform Until 2100
0.15
Expenditures, Benchmark
Tax revenue
0.1
0.05
2000
2010
2020
2030
2040
2050
2060
2070
2080
2090
Time
Panel c: Government Debt as a Share of Urban Earnings
2100
2110
2100
2110
2
0
Delayed Reform Until 2100
−2
Benchmark
2000
2010
2020
2030
2040
2050
2060
Time
2070
2080
2090
Figure C-2: Panel (a) shows the replacement rate qt for the case when the reform is delayed until 2100
(solid line) versus the benchmark reform (dashed line). Panel (b) shows tax revenue (blue) and expenditures
(black), expressed as a share of aggregate urban labor income (benchmark reform is dashed and the delayuntil-2100 is solid). Panel (c) shows the evolution of government debt, expressed as a share of aggregate
urban labor income (benchmark reform is dashed and the delay-until-2100 is solid). Negative values indicate
surplus.
Wage Rate in Rural and Urban Sectors
3200
Urban
Wage Rate (Log Scale)
1600
800
Rural
400
200
100
2000
2010
2020
2030
2040
2050
Time
2060
2070
2080
2090
2100
Figure C-3: The figure shows the projected hourly wage rate per unit of human capital in urban (dashed
line) and rural (continuous line) areas, normalized to 100 in rural areas in 2000. The process is the endogenous
outcome of the general equilibrium model of section VI.
UBS International Center of Economics in Society
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Economics. For Society.